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Copyright N° 


COPYRIGHT DEPOSIT. 









MILITARY MAPS 
EXPLAINED 


BY 

CAPTAIN H. E. EAMES, 

10th Infantry. 

Instructor, Department of Engineering, 
Army Service Schools, Fort Leav¬ 
enworth, Kansas. 



Franklin Hudson Publishing Company, 
Kansas City, Mo. 




isl 


Ufc'tARY of CONORfSS 
iwu Uopies rtectiu^ 

AUG 21 

| UUM.V> l|flM fcliW 

0‘S 

Classy (X aac. nu. 

IT I ^ 1 <1 0 

COfY B. 

Jam^*****" 0 '»^«—ViMUUuiitn -. ■ IHOJ 


< \ 

T \ ^ 


Copyrighted, 1908, by 

FRANKLIN HUDSON PUBLISHING CO., 
Kansas City, Mo. 









CONTENTS. 


Page. 

1. The Use of Maps in War. 9 

The development of topography compared to the develop¬ 
ment of war. 

Historical review’ of methods of expressing relief on maps. 

The hachured map obsolete; the contoured map the mod¬ 
ern map. 

Importance to American officers of a study of map-reading. 

The dependence of military commanders on maps. 

Meaning of “map-reading” and the application required to 
master it. 

2. Conventional Signs. 15 

The use of conventional signs at home and abroad. 

The tendency to diminish the number and variety of signs. 

The increased use of abbreviations. 

The essentials of map-reading. 

3. The Scale of the Map. 18 

Meaning of “scale,” and three ways of expressing it. 

How to construct a reading scale for a map. 

To find the R. F.; to find the number of inches to the mile 
and the number of miles to the inch. 

To construct a reading scale in familiar units from a graph¬ 
ical scale in unfamiliar units. 

To construct a scale of minutes marching. 

To measure distances on a map with a reading scale. 

To measure distances on a map with dividers; with map- 
measurer. 







4 


Contents. 


Page. 

The importance of the practice in estimating distances on 
a map. 

Problems in scales. 

4. The Determination of Directions. 4 2 

The meridian. 

The cardinal points of a compass. 

Estimating directions. 

Three purposes of contours. 

Determining the elevation of a point on a contoured map. 

5. Contours. 49 

What they are and what they show of slopes. 

Not sufficient to know that a slope is “steep” or “gentle,” 
but how steep or gentle. 

The scale of map distances for reading slopes. 

The triangle of reference. 

Three methods of reading slopes. 

Reading slopes with a scale of yards. 

Reading slopes with a scale of inches. 

Reading slopes with a slope-card, or scale of map distances. 
To construct a slope-card, by calculation, graphically. 
Problems in reading slopes. 

Slopes in “degrees” and in “gradients.” 

Converting gradients to degrees. 

Table showing influence of slopes on movement of troops. 

6. Visibility. 73 

Importance of problems in visibility. 

Convex and concave slopes. 

Determining visibility by drawing a section. 

The extent of an invisible area—limit of invisibility. 
Calculating visibility; by comparative gradients, by similar 
triangles. 

Calculating the height of objects just visible, of the point 
where the line of sight pierces the ground. 





Contents.] 5 

Pagb. 

Calculating visibility by comparison of distances and alti¬ 
tudes. 

Importance of constant practice in these problems. 
Determining the visible area on a map. 

Practical value the field of visibility problems. 

7. Problems in Visibility. 90 

Road reconnaissance reports from a m^.p. 

Influence of grades and road-beds on the tractile power of 
animals. 

Placing troops on the map 

8. Map-Reading in the Field.119 

What constitutes map-reading in the field. 

Orienting the map. 

Magnetic and true meridians. 

How to orient a map with a compass. 

Meaning of “orienting” a map. 

Orienting the map without a compass. 

Determining the magnetic variation. 

Identifying your position on a map. 

The map in close country and as a guide. 

How to carry the map. 


9. Additional Problems in Map-Reading. 129 

Appendix I.—Abbreviations Used on Foreign Maps.135 

Appendix II.—Comparative Lengths of Foreign Measures.142 


Map I. —Fort Leavenworth and Vicinity. (Two Sizes.) 

Map II. —Angelica (N. Y.) Quadrangle, U. S. Geological Survey. 









PREFACE. 


The increased use of maps in our Service, 
both in map problems, map maneuvers (War 
Game, or Kriegsspiel), and in the annual ma¬ 
neuvers in Federal and State camps of instruc¬ 
tion, would in itself increase the importance to 
officers and non-commissioned officers of the 
subject of map-reading, but the true importance 
goes beyond this in that a proper preparation 
for war presumes a knowledge of this subject on 
the part of all officers. Modern war is largely 
fought on maps, and the Art of War is, to a 
large extent, taught in time of peace by means 
of situations assumed in connection with maps. 
Many officers have never given this study the 
amount of attention that it deserves, and many 
others have forgotten the instruction they re¬ 
ceived in it at the U. S. Military Academy, and 
it is in the hope of assisting both classes to ac- 



8 


Preface. 


quire the necessary facility in map-reading that 
the following pages were written. 

The explanations are made as simple and as 
practical as possible, so that one may take up 
the study from this text without previous prep¬ 
aration, but the subject is completely cov¬ 
ered, and one who has mastered the principles 
here laid down, be he Regular, Militia, or Vol¬ 
unteer, ■ will be prepared to solve all the prob¬ 
lems injconnection with map-reading that the 
fortunes of war—or of peace—may impose upon 
him. 

The author acknowledges his obligations to 
Major D. H. Boughton, General Staff, and to 
Captain E. T. Cole, 6th Infantry, Senior In¬ 
structor,''Department of Engineering, Service 
Schools, for’material assistance he received from 
those officers. 

Fori'Leavenworth, March, 1908. 



MAP-READING. 


i. 

The Use of Maps in War. 

Hand in hand with the development of the 
science of war has advanced the science of To¬ 
pography; and as war emerged from the do¬ 
main of art into the cold, true atmosphere of 
science, soldiers have placed more and more re¬ 
liance upon the cartographer’s representation of 
the theater of operations. 

Up to the beginning of the seventeenth cent¬ 
ury, maps were either purely geographic or were 
geographic maps on which attempts were made 
to show hill features and other topographical in¬ 
cidents by pictorial effects, rather than by the 
exact methods of to-day. 

During the seventeenth and eighteenth cent¬ 
uries attempts were made from time to time to 



IO 


Map-Reading. 


represent the topography of the country on a 
more scientific system, which had for its basis 
the use of contours instead of the usual perspect¬ 
ive projection of hill-features. The proper use 
of a contoured map, however, required a higher 
degree of training in map-reading than was gen¬ 
erally possessed at that date, and a compromise 
was struck, which resulted in a sort of bird’s 
eye-view of the country, based on more or less 
accurately determined contours and known as 
‘‘hachuring.” This enabled the educated sol¬ 
dier to read his map with more exactness and 
still made it possible for his less diligent com¬ 
panions to understand in a general way the to¬ 
pographic characteristics of the ground. 

As a concession to the growing necessity for 
more detailed information on the map, the ele¬ 
vations of hill-tops were written in in figures, 
and an elaborate system was devised of showing 
the relative steepness of slopes by the relative 
amount of black and white lines on the map, and 
up to the present time Germany is handicapped 
by this archaic system in her General Staff maps 
of small scale. 


Map-Reading. 


i i 


France has recently broken away from the 
hachured map, but retains its best features by 
so shading the contoured map as to bring out to 
the eye the main topographic incidents. The 
United States, unhampered by tradition, uses 
the contoured map exclusively for military pur¬ 
poses; England uses it almost exclusively, and 
the modern German soldier has a pure contoured 
map of his country at a scale of 2.58 inches to 
the mile. 

An uncontoured county map, or a military 
sketch of whatever scale without contours, bears 
about the same relation to a contoured map or 
sketch that the smooth-bore flint-lock does to 
the modem high-power rifle. The hachured 
map is about as valuable—continuing the simile 
—as the earliest attempt at a rifled breech¬ 
loader. 

To the American officer, who will have the 
maps of the U. S. Geological Survey provided 
for his use, if any, the contoured map is the 
only one of importance and is the one to 
which he must accustom himself and whose 


12 


Map-Reading. 


details he must master. For, should a map 
problem be given on a hachured map, or should 
the fortunes of war make such a map the only 
one available, he, with his superior knowledge, 
will experience no difficulties with this antique 
form of hypsographic expression other than the 
vexation due to its imperfections. 

A review of the development of the science of 
war, from the period of dense formations whose 
limited extension made it possible for the com¬ 
mander to personally overlook the scene of bat¬ 
tle, up to the time of the huge Manchurian 
battle-fields ioo miles in length, where such per¬ 
sonal observation was obviously impossible, will 
show a constantly increasing dependence by the 
commander on maps. 

While it is true that even to-day in large arm¬ 
ies the subordinate commanders—brigade com¬ 
manders and lower—will use maps only to sup¬ 
plement the ground that they can see, still in 
small forces, acting independently, the map has 
become a sine qua non , upon which the com¬ 
mander will lean heavily, solving his daily prob- 


Map-Reading. 


*3 


lems much as, in time of peace, he solved a map 
problem. During the entire Russo-Japanese 
War there were but three of the large battles be¬ 
tween field-armies—Liao Yang, Sha-ho, Mukden 
.—but there were literally thousands of small 
engagements in which the map carried by the 
subordinate commanders played a vital part. 
The whole theater of war was elaborately 
mapped by both armies, and maps were issued 
to and used by even the company .officers and 
their non-commissioned officers. 

It is, therefore, necessary for all officers and 
non-commissioned officers to possess a knowl¬ 
edge of map-reading, and by this is meant, not 
an ability laboriously to dig out the meaning of 
the map, but an ability quickly to grasp the 
features of the ground from a contoured map. 
It is not sufficient that the officer should be able 
to follow a road from the map, or to determine 
distances; he must also know what the slopes 
of the ground are, the steepness of grades of the 
roads, the relative heights of hills, etc.—in a 
word, he must be able to form a perfect mental 


H 


Map-Reading. 


picture of the ground and grasp its features as 
though he were actually on the ground itself. 

This facility is not gained without much 
study, but the importance of the subject de¬ 
mands of all officers the expenditure of the time 
and labor necessary to attain proficiency, and 
the results of such diligence will well repay the 
officer for his labors. 






























4 









/ 

































































































r 











- r 


HOP FIELD VINEYARD (FRENCH) VINEYARD (GERMAN) 

Note • The above signs are very common on foreion maps Observe 

TNE SIMILARITY BETWEEN THE AMERICAN V/NEYARD AND FOREIGN NOPE. 


!*!*}*!■ 

"»i 


NATION AL-BOUNDAPY-LINE 

+ + + + + ++ + + 

GERMAN MAPS FRENCH MAPS 


IjX German 

French 

WATER MILL 


American 


German 


TRENCHES 


X Omen car, 

German 

QUARRY 


MILITARY 5IGM5 




Note The above shows the same slopes expressed by contours and by 
hachur.es (muffling system), [n a ‘normal SYSTEM of CONTOURS THE (MM.) 
INTERVALS SHOWN ABOVE REMAIN THE SAME FOR ALL SCALES /n THE 
RT777 GERMAN MAPS , THE NUMBER OF LINES TO THE cm IS DOUBLE THAT 
SHOWN ABOVE , AND FROM B'TO 45° THE SLOPE /S SHOWN BY MOL/D LINES 

Observe that troops can maneuver on ground where the slope /s shown 

BY DOTTED LINES AND ONLY W/TH DIFF/CULTY WHERE LINES ARE SOL/D. 

T DOTTED CONTOUR (& n) SHOWS WHEPE THE SLOPE CHANGES. 








































































CONVENTIONAL SIGNS 


RAIL ROADS 




^4 




vitMiull 


SINGLE SIDINGS. DOUBLE FILL. TVNNEL CUT. 

"Note: On GOME FOREIGNMftP5 RTULR0AD5 ARE SHOWN BY SOLID RED IMF, 
BUT WHERE COLOR /S MOT USED THE MOST COMMON S/GNS /?/?£ •• 

Jr&cR, and nnt w^mxmmxmJor/Doc/6/<tTitcJ(. 


'fy/rajAov 2/e* ofXnxtt/J 
I/39Z 


ROADS. 


UN IM PROVED *V PRIVATE- TRAIL PAT H 


| | IMPROVED 

"Note:Foreign poade of- tub better ceasses have rows of trees 

ON BOTH S/DES;THE PEE 5 EMCE CF THEBE TREES ON A MAP INDICATES 
A GOOD ROAD, TNI /3 - . THE NATIONAL HIGHWAYS 

APE DRAWN WITH HEAVY LINES AND INFERIOR ROADS ACCORD/NO TO 
CHARACTER, ONE SIDE EIGHT/ BOTHBIDES EIGHT; ONE OR BOTH DOTTED. 

STREAM CROSSINGS. 



FOREST 


VINEYARD 


CEMETERY 
































































































































































II. 


, Conventional Signs. 

As a knowledge of the alphabet is necessary 
! in reading the printed page, so is a knowledge of 
the topographer’s alphabet necessary in reading 
a map. This topographer’s alphabet—the con¬ 
ventional signs—varies with different maps and 
with different topographers and countries, but 
universally they are intended to be more or less 
self-explanatory, being merely a species of sign¬ 
writing, a miniature representation of the object 
expressed, or, if obscure and unusual, are ex¬ 
plained in a legend. It makes little difference 
in the printed page whether the printing is done 
in Roman, Italics, or Old English type, and as 
little difficulty will be found with the various 
conventional signs unless they are quite unusual 
or consist of abbreviations in a foreign tongue. 

The purpose of the map, the scale, the meth- 


15 





i6 


Map-Reading. 


ods of reproduction, etc., all call for variations 
of the conventional signs; those used on the 
io^To maps of Germany would be quite impos-i 
sible and out of place in a hasty military sketch 
made at 3 inches to the mile. The .tendency in 1 
modem maps, however, is to reduce the number! 
and variety of signs and substitute abbrevia¬ 
tions. This presents a real difficulty in working: 
on foreign maps, even when possessed of a slight 
knowledge of the language; though, of course, 
even a little knowledge of the language will make: 
clear many otherwise unintelligible abbrevia-I 
tions. To know, for instance, that Bahnhof is 
the German word for “railroad station” makes: 
clear at once the abbreviation Bnf. found be¬ 
side a house on the railroad In reading a German 
map. The Germans also make a great point of 
showing the character of the roads by means of 
conventional signs, but, except on the Govern¬ 
ment maps, these signs vary for roads of the 
same character. Some of the most generally- 
used foreign abbreviationsj are given in Ap¬ 
pendix I. and just preceding this chapter will 





Map-Reading. 


17 


be found a large assortment of conventional 
signs. 

Assuming, then, no great difficulty with the 
conventional signs, the essential elements of 
map-reading require that you should— 

1. Learn to appreciate distances on the 

map—grasp the scale. 

2. Learn to appreciate directions on the 

map. 

3. Learn to appreciate and grasp the 

ground forms, slopes, and undula¬ 
tions expressed by the contours on 
a topographical map. 






2— 



III. 

The Scale of the Map. 

All maps are made to scale —that is, a cer¬ 
tain relation or ratio exists between horizontal 
distances on the ground and distances on the 
map. This relation always is, or should be, 
stated on the map, but custom differs with car¬ 
tographers as to the method of its statement. 

If, for example, a distance of i mile on the 
ground is to be represented by a distance of i 
inch on the map, the relation of map and ground 
distances is as i inch is to i mile, and often that 
simple statement is made in words and figures; 
e. g., “Scale i inch = i mile.” In other cases a 
graphical scale will be given—that is, (with the 
same scale as above, i inch = i mile),a straight 
line will be divided into inches and each division 
marked with its value from left to right, the end 
of the line marked “zero,” the first inch division 


18 





Map-Re;ading. 


19 


marked “ 1 mile,” the second marked “ 2 miles,’’ 
etc. Since maps are often of international ap¬ 
plication where different systems of measure¬ 
ments would make either of these two methods 
awkward or inutile, and since various problems 
in map-reading arise which require for their so¬ 
lution a more convenient statement of the rela¬ 
tion of map and ground distance, it is customary 
on modem maps to give the relation in a frac¬ 
tional form, the numerator being unity and rep¬ 
resenting map distance, and the denominator 
representing ground distance, expressed in the 
same unit of measure as that taken for the nu¬ 
merator. This fraction is called the “repre¬ 
sentative fraction” (usually abbreviated “R. 
F.”), and may appear on the map in any of 
the following forms: ^ouu; R. F. = 2000b; Scale 
2biw; or Scale 1—20000; all meaning the same 
thing— -i. e ., 1 inch on the map represents 20,000 
inches on the ground, or that the map distances 
are 2bbbo of the length of the ground distances. 

Taking the example above considered of a 
ma£> on a scale of 1 inch to the mile, the rela- 




20 


Map-Reading. 


tion between map and ground distances is 1 mile? 
but to reduce this to the form of an R. F. } either 
the numerator must be reduced to miles or the 
denominator to inches, since both must be in 
the same unit, and further, since the numerator 
of the R. F. is to be unity, it is evident that the 
mile must be reduced to inches. A mile equals 
63,360 inches, so that the R. F. becomes ^o- 
If the scale is n inches = 1 mile, the denomi¬ 
nator of the R. F. is found by dividing 63,360 by 
n inches; e. g., 3 inches = 1 mile; — R. F. 2mo-t 
Having reduced the R. F. in this manner, it 
is of no further importance that we started with 
inches and miles, for we are concerned only with 
the relation that exists between map and ground 
distances, and we know from the R. F. 
that 1 inch on the map will represent 63,360 
inches on the ground. If we measure on the 
map a distance of 1 foot (12x1 inch) we know 
that it will represent 12 x 63,360 inches on the 
ground; in other words, we can multiply both 
numerator and denominator by the same num¬ 
ber without changing the value of the fraction 



Map-Reading. 


21 


or the map-ground relation. The importance of 
this is that a foreigner, accustomed to the metric 
system and knowing only that the ratio of the 
map to the ground distances is 1—63,360, can 
consider the numerator as 1 meter, or 1 centime¬ 
ter, or 1 decimeter, or any other unit, and, with¬ 
out computation, he knows that the denominator 
is also 63,360 meters, or centimeters, or decime¬ 
ters, etc. Conversely, a foreign map made with 
a ratio of 1 centimeter to 250 meters (= 25,000 
centimeters), and so bearing the R. F. 25U00, is 
intelligible to us, for we read the ratio as 1 inch 
= 25,000 inches, and ignore the system of meas¬ 
urement used in the construction of the map, as 
we may do, since we know that the map is 25000 
of the size of the ground. 

Before we can measure distances on a map we 
must have a graphical scale in units with which 
we are familiar and in which we wish to know 
the distances, as in yards or miles. If the rela¬ 
tion of map and ground distances is expressed in 
words and figures, we must first deduce the R. F. 
in the manner indicated; if a graphical scale only 




22 


Map-Reading. 


is given and that in unknown units, such as Prus¬ 
sian fuss, meters, etc., we must first find the 
length in familiar units of a Prussian fuss, a 
meter, etc., and then either construct the de¬ 
sired scale graphically or deduce the R. F. 

Having obtained the R. F., the problem of 
constructing a graphical scale becomes a simple 
matter of arithmetic. Suppose the R. F. is 
6 l^o, and we wish a scale to read yards. We 
know that i inch on the map represents 63,360 
inches on the ground, and that, since there are 
36 inches in 1 yard, 1 inch will represent as many 
yards as 36 is contained times in 63,360, or 1,760 
yards. An inch scale, with its divisions marked 
zero, 1,760, 3,520, 5,280 yards, etc., may at once 
be made, but this would be an inconvenient 
scale to use, for with it we could measure these 
and no other distances. The problem, then, be¬ 
comes one of constructing a scale with which we 
can measure any distance to within say 100 
yards. Now, if 1,760 yards are represented by 
1 inch, 5,000 yards will be represented by a line 
as much longer than 1 inch as 5,000 is greater 




Map-Reading. 


23 


than 1,760—that is, 1 inch : finches :: 1,760 : 
5,000, from which x = 2.84 inches. 

Consideration of the above proportion will 
show that the first terms (1 : x inches) will re¬ 
main constant in any and all problems, and that 
the value of x can always be found by dividing 
the desired number of units by the number of 
similar units represented by 1 inch. From the 
first and second steps of the problem above de¬ 
tailed we can form the following simple rules for 
constructing a graphical scale from a given R. F.: 

(a) Divide the denominator of the R. F. 

by the number of inches in the de¬ 
sired unit of measure. 

(b) Divide the desired whole reading of 

the scale by the quotient found by 
(a), the result will be the length in 
inches of a line representing the 
desired whole reading of the scale. 

Example .—The detailed maps of Germany 
are made with an R. F. of 25^06- Required a 
scale of vards: 

(a) it =694.44 

ip) 694.44 - 5 -°3 





24 


Map-Reading. 


A line 5.03 inches long on the map will rep¬ 
resent 3,500 yards on the ground. Even this 
may be simplified and the sometimes long arith¬ 
metical calculations avoided by performing both 
(a) and ( b ) at the same time, thus: 


3500 

25WUU - ^500 

30 1 


36 

35000 


25 = 5-°3 


The question of how long to make the scale 
is involved in the above examples, in the first of 
which 5,000 yards was arbitrarily chosen and in 
the latter 3,500 yards. Of course, the only im¬ 
portance the question can have is, whether the 
resulting length of line will be long enough for 
the probable use of the scale, for if too short, 
troublesome repetitions of measurement become 
necessary, and if too long, the division into 
smaller parts is awkward. The student should 
not be misled into the belief that “about 3 
inches,” or “4” or “6” inches is the correct 
length for a scale, but rather from a knowledge 
of the probable use of the scale, and above all 
from experience, settle each case on its own mer¬ 
its. If, as in the last example, a line about 5 



Map-Rkading. 


25 


inches long is desired, it is seen from inspection 
that if 1 inch = 694.44 yards (nearly 700 yards), 
a line 5 inches long will represent a little less than 
5 x 700 or 3,500 yards, which was the length 
I chosen above. If, on the other hand, the use of 
. the scale will be such as to seldom call for meas- 
r urements of over 3,000 yards—as in taking off 
rifle-ranges—3,000 or 3,500 yards is chosen, and 
the resulting length is allowed to work itself out. 

With the whole length known (5.03 inches = 
3,500 yards) and a line 5.03 inches long drawn, 
it still remains to divide that line into convenient 
graduations. This may be done by calculation 
or graphically; in either case the graduations 
would be so placed as to read whole numbers, as 
500 or 1,000 yards, and the left-hand division, 
equal in length to the others, would be still 
further subdivided to read to as small a distance 
as possible in view of the scale of the map. Let 
us say that the main divisions are to be 500 
yards apart; then, since 3,500 yards are shown 
by a map distance of 5.03 inches, 500 yards 
would be shown by \ of 5.03 inches, or 0.72 of an 





26 


Map-Reading. 


inch. Draw a line and mark, with the aid 
of a scale of iJo or ^7 inch parts, a series of 
points 0.72 inch apart from left to right, each of 
which will represent 500 yards. Mark the left 
end of the line 500, the first division o, the sec¬ 
ond 500 yards, the third 1,000 yards, etc., to the 
right-hand end. Now divide the left-hand space , 
into five parts, each £ of the length represent¬ 
ing 500 yards (f = .145) and each representing 
£ of 500 yards, or 100 yards, and mark them 
successively 400, 300, 200, 100 yards, as indi¬ 
cated below: 

500 O 500 1000 1500yds. 

I 400 300 ZOO 100 [ I I I 

Plate 1 

If lacking a suitable scale of equal parts, di¬ 
vide the 5.03-inch line into seven equal parts 
graphically and similarly subdivide the left di¬ 
vision into five parts. 

The principle upon which this graphical di¬ 
vision is based is that of similar triangles whose ; 




Map-Reading. 


27 


sides are always proportional. Therefore, if we 
form a triangle with one side 5.03 inches long 
and the opposite side 7 inches long, we can con¬ 
struct seven similar triangles within it whose 
sides will be proportional: 



Draw the horizontal line AB 5.03 inches long, 
and at any convenient angle with it draw AC 7 
inches long, and connect B and C. The line AC 
is easily divided into seven divisions by the inch 
scale, as shown at a, b, c, d, e, f, and g. Draw- 





28 


Map-Reading. 


ing lines parallel to BC from these points, as in¬ 
dicated by the dotted lines in the figure will 
form seven similar triangles, in the first of 
which the side A a will be to the side AC as i by 
construction; the other sides will bear the same 
relation to the triangle ABC, and the distance Ai 
will therefore be to the distance AB as I; the 
second triangle will be *, etc., to the end. 

In this construction the line a i is | of BC, 
etc., but the length of the side BC does not enter 
into the problem, and it is immaterial what the 
length of that side has been made, or, which is 
the same thing, at what angle AC is drawn with 
reference to AB. The important thing is to 
make AC of such a length (not too widely differ¬ 
ing from AB) that it shall be readily divisible 
into the desired number of parts and that the 
parallel lines be truly parallel, for otherwise the 
triangles will not be similar nor the sides pro¬ 
portional. 

In deducing the R. F. from the form of a 
statement, it should be observed that while no 
rule exists as to the relative position of map and 


Map-Rdading. 


29 


ground distances, the part of the statement 
which gives the map distance can always be 
known by the relative smallness of the unit in 
which it is expressed. Thus the expressions “3 
inches = 1 mile” and “3 miles = 1 inch” are 
both correctly expressed, although the position 
of the map distance with reference to the sign 
of equation is exactly reversed. The expres¬ 
sions cannot well be misunderstood, however, 
since it would be manifestly impossible to meas¬ 
ure miles on the map to find inches on the 
ground. Representing the same ground, the 
first map would be nine times as large as the 
second. 

It has been stated that where the number of 
inches to one mile is given, the R. F. is found 
by dividing 63,360 (inches in one mile) by the 
number of inches to the mile of the scale; e. g., 

Scale 3 inches = 1 mile, 63 f° =21,120; R. F. = 

1 

21120- 

Where, however, the number of miles to the 
inch is given, the R. F. is found by multiplying 
63,360 by the number of miles to the inch; e. g.. 


3« 


Map-Reading. 


3 miles = i inch, 63,360 X 3 = i 9 °> o8 °; R - F. 

= 190080- 

Another case will arise, however, where the 
R. F. is given and it is desired to know (1) the 
number of inches to the mile, or (2) miles to the 
inch. (1) Divide 63,360 by the denominator of 
the R. F., or (2) divide the denominator of the 
R. F. by 63,360; for example: 

(1) R. F. 2iko = ini = 3 inches to 1 mile. 

(2) R. F. 19^80 = HSr =3 miles to 1 inch - 

Under the second system of scale statement 

—the graphical scale—it has been stated that 
the length of the new scale in familiar units may 
be found graphically or by computation. For 
example, a foreign map has only a graphical 
scale of versts. By reference to a table of com¬ 
parative measures a verst is found to equal 
0.6629 statute miles. The scale is then meas¬ 
ured, and it is found that a distance of 5 versts 
is represented by 2.1 inches. If 2.1 inches = 5 
versts, 1 inch will represent o versts, or 2.38 
versts. A verst is 0.6629 statute miles long, or 
0.6629 x 63,360 inches = 42,001.344 inches, 


Map-Reading. 


3 1 


which we may call 42,000, and if 1 inch = 2.38 
versts, as above, it will equal 2.38 x 42,000 = 
99,960 inches, and the R. F. is §9^. 

In the foregoing computation we disregarded 
the smaller decimal places, in view of which and 
of the fact that the R. F. is seldom a fraction¬ 
al number, such as 99,960 (which differs from 
100,000 by only 40), it is evident that the R. F. 
is ioSmo, and this may be verified by carrying 
out each result to say four decimal places, when 
the R. F. will be found to be 99999:9999293- 




32 


Map-Reading. 


Graphically, the solution is simpler (Plate 3): 
Reproduce the given scale of versts on a hori¬ 
zontal line; measure on this line, using any scale 
of equal parts 6.629 divisions (AB); draw at any 
angle the line AD and lay off 10 divisions (AC); 
connect B and C. A line parallel to BC at the 
5-verst mark prolonged to meet AD will give the 
distance AD as 5 miles. Smaller divisions of the 
verst scale are converted into miles by a series of 
parallel lines, as indicated. 

From the properties of similar triangles it is 
seen that the distance AE (== 5 versts) bears the 
same relation to AD (5 miles) as 0.6629 mile 
(value of 1 verst) does to 1 statute mile. 

Thus far we have considered only graphical 
scales reading units of linear measure. It is 
often necessary, however, especially in map 
problems or in map maneuvers, to construct 
scales that shall read minutes of time marching. 
This introduces no new principle, but an appli¬ 
cation only of those explained. For example, it 
is desired to construct a scale of minutes for in¬ 
fantry marching, and it is assumed that infantry 


Map-Reading. 


33 


marches 21-2 miles per hour, including halts. 
The R. F. is 1 rnu- At this scale 1 mile is shown 
by 3 inches and 2% miles by 2\ x 3 = 7.5 
inches. Draw a line 7.5 inches long and divide 
it as desired—into 4 parts to show 15 minutes 
each, the left division subdivided into 3 parts to 
show 5 minutes, or divide it into 12 parts to 
show 5 minutes each, the left space divided into 
5 parts showing single minutes. The length 
in inches of the spaces in the latter case will 
be = .625 inch, and in the former = 1.875 
inches. 

If a scale of yards has been prepared, it will 
be easier, perhaps, to find the number of yards 
traveled in 1 minute and to lay off this distance 
with the scale of yards. Thus: 2.5 miles = 
4,400 yards (2.5 x 1,760), and lo" = 73J yards 
traveled in 1 minute. This is too small to lay 
off with accuracy, so lay off 367 yards to show 5 
minutes (5 x 734— 367). 

Having by one of these methods constructed 
a scale on a strip of paper, distances are meas¬ 
ured by applying the scale to the required por- 


34 


Map-Reading. 


tion of the map, placing one of the divisions of 
the main scale opposite the right-hand end of 
the line to be measured and adding to the read¬ 
ing of this whole number such fractional part as 
the subsidiary scale shall]indicate. 


s 



In Plate 4 it is desired to read the distance 
from the bridge to the church. Placing 800 at 
the church, the left end of the scale does not 
reach the bridge; with 1,200 at the church, the 
zero is beyond the bridge; but with the 1,000- 
yard division at the church, the bridge is oppo¬ 
site the secondary scale, as it should be, and a 
closer inspection shows it to be opposite the 
graduation of 125 yards; this, added to the 
1,000 yards of the main scale, gives the whole 
distance as 1,125 yards. This will make it plain ij 







Map-Reading. 


35 


why the secondary scale covers one complete di¬ 
vision of the main scale and why it is numbered 
in the reverse direction. 

Distances are measured on a map in the man¬ 
ner indicated, only when the absolute distance 
is required and the scale has been constructed 
on or transferred to a strip of paper. In prac¬ 
tice, if a graphical scale is on the map, it is cus¬ 
tomary to use a pair of dividers to transfer the 
distance from the map to the scale. Dividers 
cost from 5 cents to $5.00, according to design 
—and the 5-cent kind will prove about as satis¬ 
factory as the more expensive for this class of 
work. In using dividers, one leg or point is 
placed on one extremity of the line to be meas¬ 
ured and the dividers are opened until the other 
leg rests on the other extremity; then, being 
careful that no further movement takes place in 
the instrument, the points of the dividers are 
placed, one at the proper division of the main 
scale, the other falling on the secondary scale, 
and the distance read as explained for a portable 
scale. 


36 


Map-Reading. 


Where the distance to be measured is not 
along a straight line, as where it is desired to 
know the distance along a winding road, each 
straight section must be considered by itself and 
the lengths of the successive straight sections 
added. With dividers this is done by first ex¬ 
tending the dividers to include the first straight 
stretch, then pivot the instrument on that leg 
which rests on the road’s first change of direction 
until the plane containing the two legs also con¬ 
tains the second section of road; the free leg is 
then placed on the paper, the pivot leg raised 
and extended to the next turn, etc., to the end. 

In Plate 5 it is desired to measure the road 
distance from a to d. (1) Open the dividers 
from a to b, pivot on b until the free leg lies in 
prolongation of be (at a') and set it there, lifting 
the leg from 6; (2) open the legs still wider to 
include a'c, pivot on c until the left leg rests at 
a", open to d. The distance from one leg to 
the other will now be the whole (road) distance 
from a to d, which may be referred to the graph¬ 
ical scale, as explained. 


Map-Reading. 


37 


Using a portable scale, the same method is 
followed: Lay the scale along the road from a 
to b, the zero of the scale at a, holding the scale 
at b by a pin or pencil-point, turn it on b until 
it lies along be, pivot again at c , and mark on the 
map the position and value of the last main di¬ 
vision between c and d\ read the distance from 
this mark to d by the secondary scale, and add 
to the whole reading. 

When much of this sort of measuring is re¬ 
quired, the process becomes tedious and is sim¬ 
plified by using a curvimeter, or map-measurer. 
The curvimeter is an instrument having a small 
wheel, which is rolled along the road, its motion 
translated through a train of wheels within the 
case to a pointer like a watch-hand. This point¬ 
er moves around a dial graduated, usually, so as 
to record the distance in inches and also in cent¬ 
imeters traveled by the instrument along the 
road. The ground distance may thus be com¬ 
puted if desired, or, moving the instrument 
along the graphical scale in an opposite direction, 
the hand will return to zero when it has trav- 


38 


Map-Reading. 


eled the original distance. By noting this dis¬ 
tance on the graphical scale, its value in ground 
distance becomes at once known. Curvimeters 
are made in two patterns, one having a small 
pencil-like handle and the other the general 
form of a small watch. They cost from $1.25 
to $2.00, and are very convenient. 



Having thus constructed a graphical scale, 
familiarize yourself with it, master it; practice 
by estimating the distance from one point on the 
map to another, and check your estimate by the 
scale. Ask yourself, “Is this point within ar¬ 
tillery range from that hill?” “Is this house 
within effective infantry range of the bridge?” 




Map-Reading. 


39 


‘ ‘ How long would it take infantry to march from 
‘here to there’ ?” etc. Make your estimate, 
check it by the scale, and continue and re¬ 
peat until you are able to estimate the distance 
with an error not greater than i of the true 
distance. 

In this way you will soon be able to scale 
distances with the eye with surprising precision 
—an important and vital step towards profi¬ 
ciency in map-reading. Having mastered the 
scale of a large-scale map, but not before, take 
up a small-scale map and repeat; return to the 
large scale, and alternate until varying scales 
present no difficulty to you. 

Examples. 

1. The scale of a map is i inch to the mile. 
What is its R. F. ? 

2. The scale of a map is 4 inches to the mile. 
What is its R. F. ? 

Answer: -f° = 15,840: R. F. = j^. 

3. The scale of a map is 5 miles to the inch. 
What is its R. F. ? 


40 


Map-Reading. 


Answer: 63,360 X 5 = 316,800: R. F. 31^00. 

4. The scale of a map is 2^ miles to the 
inch. What is its R. F. ? 

5. The R. F. of a map is e^uo. Express the 
scale in inches to the mile. 

Answer: R. F. = dw = US = 1.012 inches 
to the mile. 

6 . The R. F. of a Japanese map is 2500b. 
Express the scale in inches to the mile. 

7. The R. F. of the German General Staff 
map is nx^uu- Express the scale in miles to the 
inch. 

Answer: R. F. = io^juo = = 1.5 8 miles 

to the inch. 

8. Express the R. F. in inches to the 
mile. 

9. The R. F. of a map is given as 1^00. 
Construct a graphical scale to read miles. 

10. The R. F. is given as 3212b. Construct a 
graphical scale to read yards. 

11. A German map bears the following 
scale of German geographical miles. Construct 
a scale to read statute miles (English). Note. 


Map-Reading. 


41 


— 1 German geographical mile = 4.61 miles 
(statute). 

012 

!_|_l 

Geographische Meile. 

12. On a portion of the map of Fort Leaven¬ 
worth the distance along Grant Avenue from 
Augur Avenue to Metropolitan Avenue is found 
to be 19.7 inches. It is known that this dis¬ 
tance on the ground is 8,668 feet. What is the 
R. F. of the map? 

a 19.7 inches '19.7 inches 19.7 1 

Answer: ~msleet == 8668 x 12 inches 104016 = 5280 

= R. F. 

13. Draw a scale to show minutes of cav¬ 
alry marching, trot and walk alternating (5 
miles per hour), for the above map of Fort 
Leavenworth. 

14. How many inches to the mile is the 
above Fort Leavenworth map? 





IV. 


The Determination of Directions. 

Having mastered the scale of the map, the 
next matter that will demand your attention is 
that of directions. Note the meridians of the 
map, both true and magnetic, if both are shown, 
and pay particular attention to the magnetic 
meridian, since it is this line of reference that is 
used with the compass, and not the true me¬ 
ridian. In map-reading indoors, or even in 
field map-reading, unless the position of the 
magnetic meridian is quite at variance with the 
true, it will be sufficient to refer directions 
roughly to the true meridian, though, as will be 
explained later, the magnetic meridian may be 
the only one that should be used, under certain 
circumstances. 

In Government maps, and indeed in most 
maps, no meridian at all is drawn, the side 


42 


Map-Reading. 


43 


border-lines serving as such, or even the letter¬ 
ing, which is done on an east-and-west line. A 
small triangle and a note, both showing the 
magnetic variation often appear in the mar¬ 
gin, especially on Government maps. 

There are two methods of graduating the 
compass circle: (i) into degrees and (2) into 
“cardinal points/’ 

(1) The whole circle, divided into 360 
equal parts, each of which will represent a “de¬ 
gree” (shown thus: °), is used in map-making 
and sometimes in map-reading. 

(2) The whole circle, divided into 32 parts, 
each of which represents a “point,” is used in 
map-reading and in orders, but never in map- 

1 360 

making. Each point is equal to 11J 0 fe = 
11J), and with this knowledge it is easy to 
convert “points” to “degrees,” and vice versa. 

A reference to the following plate will show 
that the primary divisions are 4: N., S., E., and 

W. The intervals between these points are di¬ 
vided, producing 4 more points: N. E., S. E., 
S. W., and N. W. The intervals between these 


44 


Map-Reading. 


secondary divisions are again divided, and these 
are named, with reference to the secondary di¬ 
visions, N. E., S. E, etc. Thus the point midway 
between the N. and N. E. points is called 
N. N. E.; that between the N. E. and E. points 
is called E. N. E., etc. Lastly, the intervals be¬ 
tween the 16 points described are divided into 
what are called the “by” points, since the word 
“by” occurs in all of them, and, on the prin¬ 
ciple that as they are on or by the N., S., E., or 
W. of the first 8 divisions, they are designated 
that division “by N.,” “by E.,” etc. Thus, on 
each side of the N. point is a “by” point, one 
being N. by E., the other N. by W. Beside the 
N. E. point are the N. E. by N. and the N. E. 
by E. points, etc. 

In map-reading it is seldom necessary to be 
so exact as to require the use of the “by” 
points, and when the occasion does arrive, it is 
best to give the direction in degrees. The car¬ 
dinal points will frequently be used to the first 
8 divisions, and in special cases to the first 16 
points. 


Map-Reading. 


45 


Having found the meridian, draw one across 
the map to guide you in practicing estimating 
directions. Mark a spot on the map where you 



tered there with the cardinal points on it. Es¬ 
timate the direction in terms of the cardinal 
points of the compass, and check your estimate. 
This you can do if you first orient the map and 





46 


Map-Reading. 


then apply the compass to the assumed station, 
making the sighting-line on the box-lid point to 
the spot to which you have estimated the direc¬ 
tion. To orient the map, lay it on a table, place 
the north-south line of the compass parallel to 
the meridian, and revolve the map and compass 
together until the needle points to the zero of 
the compass. The map is now oriented, and 
should not be disturbed. Having estimated a 
direction, lift the compass to the spot you 
marked as being your location, and sight along 
the line on the lid of the box (moving the com¬ 
pass, but not the map) until it points to the 
place and shows the error, if any, of your 
estimate. 

Repeat this operation until you can speak 
with certainty of the “ridge 1,500 yards N.N.E. 
of our position,” etc., for nothing causes so 
much confusion as looseness in speaking of 
directions—saying “south of Hill 296” when 
“south-west of Hill 296” is meant, or “south¬ 
west” when “ south-south-west ” is meant. 

Combine the exercises in estimating distance 


Map-Reading. 


47 


with those of estimating directions as a matter 
of further practice. 

The real difficulties of map-reading come 
after these preliminaries—questions of relative 
heights, undulations of the ground, steepness of 
slopes, visibility of one point from another, etc. 
A knowledge of the principles of contouring is 
necessary to enable one to understand this part 
of map-reading. 

Contours serve three great purposes: 

1. They show the elevation of any given 

point on the ground with respect 
to all other points. 

2. They graphically represent the gen¬ 

eral undulations of the ground. 

3. They show the inclination of slopes, 

both in general terms of steepness 
and in absolute degrees of slope. 

The elevation of any point, if on a contour, 
is that of the contour, and the difference of ele¬ 
vation between two points, each of which is on 
a contour, is the difference of elevation of those 


48 


Map-Reading. 


contours. The elevation of a point not on a 
contour is proportional to its distance from a 
contour. Thus, a point half way between the 
820 and 840 contours would be 830, or \ the 
contour interval above the lower contour. If 
the point is \ the distance and nearest the 820 
contour, its elevation would be 825, or \ of a 
contour interval higher than 820. 

Here, as in the third service of contours, it 
is necessary to understand that in contouring it 
is assumed that the slope of the ground between 
two adjacent contours is uniform. This is not 
really the case, and a slight error is introduced 
by the assumption, the.error diminishing as the 
contour interval decreases, but the error is so 
small for a suitably contoured map that it may 
well be neglected. 


V. 


Contouring. 

Contouring is a method of exhibiting relief 
of ground by means of lines so drawn on a map 
as to indicate points of equal elevation. The 
lines so drawn on a map are called “contours.” 
The difference of elevation of points on adjacent 


k 



contours is called the “contour interval,” and is 
usually constant for all the contours on the 
same map. 


4- 


49 







50 


Map-Reading. 


Suppose that in digging a canal a hill were 
encountered, and that in cutting through the 
hill the sides of the cut were made perfectly 
vertical. One riding on the canal would see 
one of the banks much as is shown in Plate 6, 
where the various strata of rock are clearly seen. 
Let us suppose that the strata are all of uniform 
thickness—say ten feet each, and that they lie 
perfectly horizontal, as shown. 

The drawing of this side of the cut would be 
a section of the hill along the line of the canal, 
and by examining it we can see the steepness of 
the slopes at any point. It is manifestly impos¬ 
sible for a surveyor to go about digging canals 
in order to secure slope and elevation data for 
making his map, and even if we assume that he 
has, by any method, gained the necessary in¬ 
formation, it is still necessary that he should 
devise a way^of showing that information on 
the map. 

Suppose that he has located the point a on 
his map, which is where the bottom of the gran¬ 
ite stratum crops_out ? He might drive a stake 


Map-Reading. 


51 


at a and proceed to b, the top of the granite 
stratum, drive another stake and locate it on 
his map, and so proceed to the top, driving 
stakes at each stratum and plotting the positions 
of the stakes on his map until he has reached 
the top of the hill. His plot would look like 
this: 


a bed c fghihlm nopq r 

Q-6G0—© - 00000 —e—e— 0000 -© 

0 000 0 0000100 0 0000 0 

^ NlOT 1 K) O K I' I" 10 'flvWN i-« 

Plate- 7 . 

a would be 10 feet above the level of the can¬ 
al, b 10 feet higher or 20 feet above the canal, c 30 
feet, d 40 feet; e and f are on the same level as 
d and so are each 40 feet above the water, g is 
50 feet, h 60, i 70, and k 75. Now, going down 
the other side, l is level with i and is therefore 
70 feet, m is level with h and so 60, n is 50, 0 40, 
p 30, q 20, and r is 10 feet above the water-level. 
All this is shown in Plate 7 by the figures 10, 20, 
30, etc., opposite the plan of each stake. 

If, having located and plotted his stakes, as 



52 


Map-Reading. 


explained, the surveyor moves io feet to the 
right or left and repeats the operation on a par¬ 
allel line, his map would perhaps look like this 


C 



g'W i' T m' n' o' p' q' r n 

-o-o-o-o—o—o—o—o—o—o-D 

00 0 Ooooooo 

to vO ^ 


A-o 

iJ 


javAJ 

ooo 

MW 


V M- 'W •= 

0 0 0 0 p 

io <0 ^ 


e oa. TT 
,0 0 0 0. 
10*10^ 


0-3 

u 


Plate 8. 

The last section would, of course, be different 
from the first, but a and a' would be on the same 
level, and if a line were drawn connecting them, 
every point on that line would have the same 
elevation as a or a' — i. e ., io feet above the 
water of the canal, and such a line would be a 
contour. If every point on the first section 
were similarly joined to every point of same 
level on the second section, what has been said 
of the line a a' would be true of those other 
joining lines, which would be 20, 30, 40, etc.. 






Map-Reading. 


53 


feet above the water, and the map would look 
like this: 



a and a' can be connected, b and 6', c and c 
but the two 40-foot levels at d and at e do not 
extend to the new line; / and /' can be joined 
and all of the others. Now, looking at Plates 6 
to 9, let us see what we can find out of the slopes 
by an inspection of Plate 9. 

The slope (Plate 6) from a to b is rather gen¬ 
tle; in Plate 9 these stakes are shown far apart. 
From b to c (Plate 6) the slope is steep, and in 
Plate 9 the stakes are near together. A further 
comparison will show that this is a general rule— 
gentle slopes and distant stakes, steep slopes and 







54 


Map-Reading. 


close stakes; verify this by the slopes from l to 
n as compared with those from n to q on the 
line AB. 

Looking now at Plate 9, imagine yourself 
starting at A to walk to B. First you walk up 
a gentle slope to b, where the slope grows steeper 
as far as d. From d to / is nearly level, but from 
the existence of the stakes at d, e, and f we know 
that the ground half-way between d and e must 
be either a little higher or lower than d and e; 
as you have been going up a hill, it is evidently 
a little higher, but not high enough to receive 
the 5o-foot stake. Having passed this hill-crest, 
you have to go down to reach e and you can see 
that beyond f the slope is rising; therefore, you 
will go down to a point beyond e, but not far 
enough to receive a 30-foot stake, and, having 
passed this lowest point, you begin to ascend to 
f (Plate 10). 


Map-Reading. 


55 



From / to k, the top of the hill, the stakes /, 
g , h, and i are about the same distance apart, and 
so the slopes between them are about the same. 
You will go from k to n along a practically uni¬ 
form slope, but from n to q the slope will be 
quite steep, growing gentle again between q and 
r. The use of the section (Plate 6) assists in 
seeing these slopes along the line AB, but now 
start at C and go to D; here you have no section 
to help you, yet you can see that from a' to k' is 
an unbroken slope, since no elevation appears 
more than once, as was the case at d, e, and f on 
the line AB; and, further, that from a' to /' the 
stakes are uniformly spaced and so show a uni¬ 
form slope. The distance from /' to g' is a little 







56 


Map-Reading. 


greater, hence the slope at this point is gentler. 
The stakes g' and h' are closer together than any 
that we have considered on this line, and hence 
show that the slope at this point is the steepest 
yet met. From h' to V is about the same as 
from a' to b', b' to c', etc., and you know that 
the slope here is about the same as that where 
you started, i' and V are on the same level, 
and, by the argument presented when we passed 
from d to e on the first line (AB), you know that 
you are passing a hilltop, ascending somewhat 
higher than 70 at i! and then descending again to 
that-level at From here to the bottom of the 
hill the stakes are uniformly spaced, and so the 
slope must be uniform. 

If you draw a line midway between A-B and 
C-D on Plate 9, you can tell what the slopes are 
along that line in a similar manner. Now, a con¬ 
toured map is exactly what we have been work¬ 
ing with, and taking such a map, drawing a line 
on it at random, you will be able to read the 
slopes passed, just as you have read them on 
Plate 9. 


Map-Reading. 


57 


If we were content to know only this: that 
“here the slope is steep and there gentle,” we 
might stop here,but ideas of steepness differ, and, 
for application of the known effect of a certain 
steepness on the movements of troops, we must 
know exactly how steep the slope is at any given 
point. In Plate 9 we saw that the slope from b 
to c was steeper than that from a to b , because, 
when we compared the distance b-c with a-b, it 
was seen to be less than a-b. If the slope from a 
to b is known to be exactly i°, then the slope b-c 
is greater (steeper) than i°; and if on the edge 
of a card you had a scale showing how fara part 
the stakes (contours) would be for every slope 
from, say i° to io°, you could try first one and 
then another of these scale distances until you 
found one that was exactly the distance of b to 
c, which, let us suppose, is marked on your card- 
scale as representing the distance apart of con¬ 
tours on a 7 0 slope. The slope from b to c would 
be a 7 0 slope, and similarly you could find the 
degree of slope at any point on the map. Such 
a scale is called a “scale of map distances” (ab- 


58 


Map-Reading. 


breviated “M. D.”), and can be made for any 
map when the thickness of the strata (caded the 
“vertical interval’’ or “contour interval,” and 
usually abbreviated “V. I.”) and the R. F. of 
the map are known. 

All map distances are measured and drawn 
as though the ground were a level plain. In 
walking up a steep slope you may actually travel 
a mile, measured along the sloping ground, but 
the plotted or map distance would not be a mile, 
but the horizontal distance corresponding to a 



Plate it 


mile at that slope. Thus, in Plate n you may 
walk from A to B, but the map distance from 
the crest of the hill to the bottom of the valley 
will be a'-b', and if that distance at the scale of 





Map-Reading. 


59 


the map represented | mile, it would be said 
that you had traveled f mile, regardless of the 
slope or of the sloping distance that you act¬ 
ually may have traveled. When the ground is 
level, as from B to C, the map and ground dis¬ 
tance will be the same, while on very steep 
ground, as from C to D, the map distance c'-d' 
may be much less than the sloping distance 
actually traveled. It will be seen that the con¬ 
verse of this proposition is true—that is, that on 
varying slopes the map distance from the bottom 
to the top of the slope is least on steep slopes, 
and approaches the maximum of distance as it 
approaches the level—in a word, it varies in¬ 
versely with the slopes. 

Every slope can, therefore, be considered as 
a right triangle, its base, the map distance (a'- 
6', Plate n), its altitude, the elevation of the 
top of the hill above the bottom (A-a'), its hy- 
pothenuse, the slope of the ground (A-B), and 
the angle at B, the degree of slope. 

Now it is known that if the angle at B is i° 
and the elevation A-a' is i foot , the distance from 


6o 


Map-Reading. 


a' to b' will be 57.3 feet. A triangle of these di¬ 
mensions is called ,the “triangle of reference ,” 
since from it all questions dealing with slopes may 
be solved. 

If, for example, the slope c'-d' (Plate 11) is 
io°, and the distance D-d' is 1'foot, the map dis¬ 
tance c'-d' will be to of 57.3 feet, or 5.73 feet. 
Again, if the slope is io° and the map distance is 
57.3 feet, the altitude D-d' will be 10 x 1 foot, 
or 10 feet. And, lastly, if the map distance 
c'-d' is 57.3 feet and the altitude (d'-D) is 10 
feet, the angle of slope will be io°; for if we di¬ 
vide the map distance 57.3 feet, which corre¬ 
sponds to a rise of 10 feet in the slope consid¬ 
ered, by 10, it will give us 5.73 feet as the map 
distance corresponding to a i-foot rise. In the 
triangle of reference we know that a rise of 1 
foot to i° gives a map distance of 57.3 feet, so 
that the slope under consideration will be found 
by dividing 57.3 feet by 5.73 feet, and the slope 
is therefore io°, as stated. 


Map-Reading. 


6 i 


Triangle of Reference. 



b 


A 


57.3 Ft = 19 . 1 _/d 3 = M.D. 

The Triangle of- Reference 
Plate 12 


c 


Formula. 


S° — Degree of slope. (Hypothenuse AB.) 
V.I. = Rise in feet. (Altitude BC.) 

M.D. = Map distance iu feet. (Base AC.) 


57.8 x V.I. 
S° 

M.D. x S° 
57.8 

57.3 x V.r . 
M.D. 


10 1 yds. x V.I. 


M.D. 

V.I. 

s° 


M.D. \ (Is ) x S 
19.1 yds 
10. 1 >ds x V.T. 
M.D. V\ds.) 


All of the foregoing will be seen by reference 
to Plate 12 and its accompanying formulae. It 
will be observed that the dimensions of the V. I. 
and M. D. are both in the same unit, but when 
in any problem the M. D. is given in yards and 
the V. I. in feet, as is often the case, it is only 
necessary to reduce the 57.3 feet of the triangle 







62 


Map-Reading. 


of reference to yards (= 19.i yards), as was 
done in the second column of the above formulae. 

With this knowledge of the triangle of ref¬ 
erence, we may read the slope at any part of a 
contoured map in one of three ways: 

1. By a scale of yards and a calculation 
with the above formulae. 

2. By a scale of inches, suitably subdivided, 
and a calculation using the above formulae. 

3. By a scale of M. D.s, showing the dis¬ 
tance apart of contours at the various slopes; 
such a scale being drawn from a series of calcu¬ 
lations based on the above formulae. 

The third of these is at once the most con¬ 
venient and the most usual, since both the first 
and second require a computation for each slope 
that is read. 

Considering the First: If the graphical scale 
for the map has been made to read yards, it is 
but necessary to scale the distance between the 
contours at the point to be read and deduce the 
slope from the above formula, S° = 

Example: The scaled distance between the; 


Map-Reading. 


63 


825 and the 850 contours is 239 yards. What is 
the slope? V. I. = 850 — 825 = 25 feet. M. 
D.= 239 yards. S° = j9 L9 2 * = 2 0 . 

The scale of M. D.s may also be made by 
the use of the scale of yards, for suppose the 
V. I. of the map is 20 feet, then the formula 

—— becomes -s 5 -, and for a i° slope 

— 1 -, which is equal to Y; so that we may 
lay off on a strip of paper 382 yards, using 
the scale of yards, and mark it i°, that being 
the distance apart of 20-foot contours on a i° 
slope. A 2 0 slope would be one-half as long 
(= 191 yards), a 3 0 slope one-third as long (= 
127 yards), etc. 

Second Method: In this method the R. F. of 
the scale must be considered—no scale of yards 
having been made—for we wish to find the slope 
where contours at the scale of the map are a cer¬ 
tain distance apart. This will be best under¬ 
stood if we first work out the scale of M. D.s by 
this method. The problem is exactly the same 
as that considered on page 23 under the subject 
of “Scales.” There we learned that to find the 






64 


Map-Reading. 


number of inches which would represent a cer¬ 
tain unit (yards were the units sought), it was 
necessary to first divide the number of inches 
represented by i inch on the map by the num¬ 
ber of inches in the unit, the result being the 
number of units (yards) shown by i inch on 
the map. In the present problem the unit, 
instead of being yards, is the base of a tri¬ 
angle whose altitude is the V. I. of the map. 
Suppose the R. F. = 21X20 and the V. I. = 
20 feet. Then from the triangle of reference 
we know that for a slope of i° the M. D. 
will be 20 x 57.3 feet = 1,146 feet, which is 
equal to 1,146 x 12, or 13,752 inches, so that 
our unit of measure is' 13,752 inches, and by the 
rule [ (a), page 2 3 ] 1 inch will represent = 
1.54 of such units, and by the rule [ (6) page 23] 
1 such unit will be represented by = 0.65 
inches. A 2 0 slope will be half as long (0.325 
inch), and a 3 0 slope 0.22 inch, etc. This 
may all be expressed by the formula M. D. = 
and so long as the 12 and the 57.3 
. of the formula remain constant, which will 



Map-RlvAding. 


65 


be the case when the V. I. is given in feet, we 
may simplify the formula by writing it M. D. = 

V ( x pg7 6 jo 

s°~xDenom.R.P., or, considering 687.6 as 688, M. D. 

_V.t. X 688_ 

S° x Denom. R.F. 


In the example just worked out the values 
become r x2 im) = 2II2U = 0.65 inch, as before. 
But the reverse of the above will occur in map- 
reading where the degree of slope is unknown 
and the M. D. is known, and in such case the for- 

, , 00 Y.I. x 688 20 x 688 

mula will become S° = m.d; x D eQom. k.f.; e. g. f 


If, then, in examining a map we find the 
R. F. = ^70. and the distance apart of two ad¬ 
jacent contours (825 and 850) to be 0.23 inch, 
the slope will be = 3°. 

Rule .—-Multiply the vertical interval be¬ 
tween contours in feet by 688 and divide this 
result by the measured distance between con¬ 
tours in inches by the denominator of the R. F. 
The result will be the slope in degrees. 

The scale of M. D.s can also be constructed 
graphically, with sufficient accuracy for military 
purposes, as follows: 








66 


Map-Reading. 


Draw two parallel lines distant' apart io 
times the V. I. at the scale of the map, and on 
the lower line construct a triangle as ABC, 
Plate 13, making the altitude BC = 1 inch and 
the base AB = 5.73 inches. 



Plate 13 


From the triangle of reference we know that 
the angle at A = io°, for the base is tV of the 
length of a base corresponding to a slope of i° 
and a rise of 1 inch. Since we have drawn the 
contour interval (D.E.) ten times too large and 
an angle of io°, whose base is tV as long as an 
angle of i°, these two dimensions will neutralize 
each other and AE, the distance from the point 
A to the point E directly below the intersection 
at D will be equal to an M. D. for a i° slope at the 








Map-Reading. 


67 


scale of the map and proper contour interval. 
A slope of 2 0 will be shown by one-half this dis¬ 
tance, a 3 0 slope by one-third of the distance 
AE, etc. 

Example: V. I. = 20 feet — 61 yards. 
Lay off the parallel lines iox6§ yards, or 66§ 
yards apart, using the scale of yards which you 
have made for the map. Draw the triangle 
as explained, base 5.73 inches, altitude 1 inch, 
and from the intersection of the slope with the 
parallel line drop a perpendicular to the lower 
parallel line. The M. D. thus found for i° may 
be divided as explained under “Scales.” 

Problems. 

1. The scaled distance between the 1,020 

and the 1,040 contours is 127 yards. What is 
the slope? Answer: = 3°. 

2. The scaled distance between the 2,500 
and the 2,525 contours is 400 yards. What is 
the slope? Answer: 1.2 0 . 

3. The scaled distance from the bottom of 


68 


Map-Reading. 


a uniform slope (elevation 1,200) and the top 
(elevation 1,325) is 795 yards. What is the 
slope? Answer: 3 0 . 

4. The R. F. == ioikro; the V. I. = 5 meters, 
the distance from the 200 to the 205 meter con¬ 
tour is 0.18 inch. What is the slope? Note: 
1 meter = 3.28 feet. 

Answer: It is first necessary to reduce the 
V. I. to feet; V. I. = 5 x 3.28 = 16.4 feet. 
The equation then becomes oisviSo = .627°. 

Had the value of the meter been given 
in inches (39.37 inches = 1 meter), this value 
would have been reduced to feet, or the numera¬ 
tor of the equation would have been written 
39-37 x 5 x 57*3» which is clear when we remem¬ 
ber how the 688 was obtained. 

5. The R. F. = 25U0O*, the V. I. = 20 me¬ 
ters; the distance from the 200 to the 220 meter 
contour is 1 inch. What is the slope? Note: 1 
meter = 39.37 inches. 

Thus far we have considered slopes only in 
terms of degrees. In work on roads, railroads, 
and rivers the inclination of the ground is often, 



Map-Reading. 


69 


if not usually, expressed in gradients —that is, in 
the form of a fraction, whose numerator is unity 
and whose denominator is the horizontal dis¬ 
tance in the same unit of measure which corre¬ 
sponds to a rise of 1 unit. We know from the 
triangle of reference that a i° slope rises 1 foot 
in a horizontal distance of 57.3 feet. The gradi¬ 
ent of a i° slope is therefore 5 }~ s , which may be 
called without introducing any appreciable 
error. A slope of 2 0 is a gradient of etc., the 
gradient corresponding to any slope being found 
by multiplying Ar by the degree of slope, and the 
slope corresponding to a gradient being found by 
the reverse process— i. e. f multiplying 60 by the 
gradient; e. g., 5 0 slope = Ar x 5 = A: and 
tV X 60 = 5 0 slope. 

Gradients are written W, or 1 in 12, or 1:12, 
and, like the R. F., express a ratio, so that any 
value may be given to its terms so long as both 
numerator and denominator are expressed in 
the same units. A gradient of W means a rise 
of 1 foot in 12 feet, and also a rise of 1 meter in 
12 meters, etc. 


70 


MaP-RIvADTNG. 


The use of gradients in map-reading is not, 
however, confined to questions of roads, rail¬ 
roads, and rivers, for if you scale the distance 
between the contours and find it to be, say 125 
yards (which is equal to 125 x 3 feet =325 
feet), this may become the denominator of a 
gradient whose numerator is the V. I. of the 
map. If the V. I. = 25 feet, the gradient would 
be £ = iV = 4 °. 

Example: The scaled distance between 20- 
foot contours is 150 yards. What is the gradi¬ 
ent and what the slope? Answer: 2 h = 2.68°. 

The practical value of slopes and gradients 
in their relation to the movements. of troops 
may be seen from the following table: 




TABLE I. 


Influence of Slopes on Movement of Troops 
and Vehicles. 

Slopes up to 5 0 

Are practicable for all arms. Cavalry will 
charge more effectually uphill than down. 
Artillery fire is more effective downhill 
than up. 

Between 5 0 and io° 

Close movements for infantry are difficult. 
Cavalry can only charge uphill a short 
distance. Artillery moves with diffi¬ 
culty; its effectual and constant fire 
ceases. A slope of 8° will almost stop 
baggage-wagons without extra horses. 

Between io° and 15 0 

Infantry can only move a very short dis¬ 
tance in order. Cavalry can only trot a 
short distance uphill and walk down. 
Artillery moves with great difficulty; 
fire ceases entirely. 

Between 15 0 and 20° 

Infantry cannot move in formed bodies. 
Cavalry can ascend at a walk and descend 
obliquely. 


71 


72 


Map-RivAding. 


Between 20° and 25 0 

Infantry can only move in extended order; 
light cavalry can only ascend and descend 
obliquely, one by one. 

Between 25 0 and 30° 

Infantry as before, but very slowly; cav¬ 
alry as before, but with great difficulty. 

Slopes over 30° may be climbed up by men 
using their hands. 



VI. 


Visibility. 

Of all the problems which arise in map¬ 
reading, probably none are so frequent as ques¬ 
tions involving visibility. “Can the bridge at 
A be seen from the hill at B ? ” “ How much of 

the river can be seen from the top of Prospect 
Hill ? ’ ’ etc. Such problems involve a knowledge 
of only so much of map-reading as we have 
passed over and furnish excellent exercises, and 
because of their value as map-reading exercises, 
and because of the grasp of the subject of map- 
reading that such problems give, practice in 
these problems is of prime importance, and 
should not be slighted by the student. 

Considering the surface of the ground in very 
broad terms, it may be said that a general sec¬ 
tion of the ground (except on a dead-level) must 
be either convex or concave. If it is convex, 
one end cannot be seen from the other, while if it 


73 


74 


Map-Rkabing. 


is concave, the ends are mutually visible (Plate 
14). Visibility thus turns on whether the gen¬ 
eral section is convex or concave. Frequently 
this may be determined by mere inspection, as 
where the slope is that shown in Plate 14 (a) or 



(c ). In these cases the contours will lie close to¬ 
gether at the bottom of the slope, as in (a), when 
the general section is convex, or close together 
at the top, as in (c), when the general section 
is concave. When the section is as shown 
in ( b ), a doubt will arise, which will require a 
little closer scrutiny, for the point B may be 
high enough to make the general section convex 
and it may not. The simple expedient of draw- 


Map-Reading. 


75 


ing the section at once suggests itself; for ex¬ 
ample (Plate 15). I s the bridge at C visible from 
A? The elevation of B is z\ contours higher 















7 6 


Map-Reading. 


than the bridge and that of A is 4§ contours 
higher than the bridge. It is unnecessary to re¬ 
produce the whole section; the point of observa¬ 
tion A, the point to be observed C, and the point 
of possible interference B, only are involved. 
Lay the lower edge of a piece of paper along the 
line A-B-C on the map, and make a pencil-mark 
opposite the three points A, B, and C. At the 
B mark erect a perpendicular 2\ units high and 
at the A mark one \\ units high, counting from 
the edge of the paper. Any kind of units will 
do: an inch scale, the ruling of a piece of fools¬ 
cap, etc.—in fact, anything that is uniformly 
spaced. Connect the top of the perpendicular at 
A with the mark on the edge of the paper at C; 
if this line crosses the perpendicular drawn at 
B, C is not visible from A (Plate 16). The same 
result will be obtained if the section of the 
line of sight is drawn as indicated by the dotted 
line (Plate 15), which, starting at the top of the 
4J unit perpendicular (A), just grazes B (top 
of the 2\ unit perpendicular), and, prolonged, 
clearly passes above C, which is invisible, since 


Map-Reading. 


77 


all below the line of sight would be hidden by the 
hill at B. 

If any other point of possible interference 
exists similar to that at B, test it as you have at 



contour indicates a very gentle slope and it may 
be gentle enough to produce a convex section. 
The question is solved by marking on the edge 
of the piece of paper the position of the 140 con¬ 
tour, as at D (Plate 16), and erecting there a 
perpendicular 4 units high, when it will be seen 








78 


Map-Reading. 


that the slope in question is not gentle enough 
to produce convexity in the general section. 
All questions as to the visibility of one point 
from another can be solved in this way. Ques¬ 
tions as to the limit of vision— -i. e.,“ point where 
the line of sight pierces the ground”—are also 
solved by this method, quickly and accurately. 

Referring to Plates 15 and 16: We have 



question arises as to how much beyond A the 
man can go and still remain hidden. Lay the 
paper’s edge along the line A-B-C, as before, 
and mark the position of A, B, and of the cross¬ 
ing of the 100 and no contours at C and E as 
indicated (Plate 17). Erect the perpendiculars 





Map-Reading. 


79 


as before—4^ units high at A, 2 \ units high at B, 
and 1 unit high at E—each corresponding to the 
number of contour intervals of the respective 
points above the lowest point. Connect the 
mark at C with the top of the perpendicular 
erected at E (thus reproducing the slope at this 
point); now connect A and B and prolong the 
line until it intersects the C-E line (at G), and 
from this intersection drop a perpendicular to 
the edge of the paper. This will make a new 
mark on the paper’s edge, which, transferred to 
the map, will show the first element of the slope 
C-E, which would be visible to an observer at 
A—' 1 ‘ the point where the line of sight pierces the 
ground.” 

It is not always convenient nor necessary to 
solve visibility problems in this manner, and re¬ 
sort is often had to one or another of the several 
methods of calculating the effect of an intermedi¬ 
ate point on the line of sight. 

One of these methods has for its object the 
determination of the convexity or concavity of 
the general section, based on gradients to the in- 


8o 


Map-Reading. 


tervening object. For example (Plate 15), the 
distance from A to B is 700 yards; from B to C 
is 500 yards; the rise in these distances is, re¬ 
spectively, 20 and 25 feet, so that the gradients 
become ^ and The upper gradient (A) is 
gentler than the lower (•*■*); hence the general 
section is convex, and C is not visible from A. 

Another method, and the one generally em¬ 
ployed, is based on the principle of similar tri¬ 
angles. Referring again to Plate 15, if a triangle 
is formed whose base is the distance from A to B 
and whose altitude is the difference in elevation 
between B and A (20 feet), a similar triangle 
whose base is twice as long will have an altitude 
twice as great (40 feet) (Plate 18). Now, if we 
take off on the edge of a piece of paper the dis¬ 
tance A-B and then move the paper along the 
line A-B-C until the A mark is at B, the B mark 
will be at a point on the map where the line of 
sight from A and just grazing B will have an ele¬ 
vation 40 feet lower than A, or 105 feet. This 
new position is beyond C (elevation 100) and is 


Map-Rkading. 


8 


higher, so that C is below the line of sight and 
invisible. 

Now consider the proposition of an observer 
at C looking toward A. The map distance C-B 
is taken as before, and means a rise of 25 feet. 
Applying this distance toward A, the first ap- 



Plate 18 . 


plication gives the elevation of the line of sight 
at its upper end as 150 (2 x 25 + 100). A is only 
145, and it is not necessary to go farther to see 
that A is below the line of sight and invisible. 

The question is often framed, however, so as 
to require a knowledge of exactly how far above 
the distant object is the line of sight, as where 










82 


Map-Reading. 


‘ ‘ The top of a monument at A is just visible to 
an observer at C. How high is the monument ? ” 
Keeping in mind the properties of similar tri¬ 
angles, the question becomes—solving by this 
method and in extension of what we have al¬ 
ready shown—to find the altitude of a similar 
triangle whose base is the distance from the end 
of the last application of the original base to A. 
One-half of the original base will give an altitude 
of one-half of 25 feet = 12 J feet. Halve the base 
by folding the marked paper, and try for length. 
It lies beyond A, and has an elevation of 150 + 
12J = 162J feet. Halve this distance by again 
folding the paper (= rise of one-half of 121 = 
6.25 feet). This falls as far short of A as the 
other fell beyond, and gives an elevation of 150 
+ 6.25 = 156.25 feet. Again halve this base in 
the same manner (= a rise of one-half of 6.25 = 
3.13), and it falls on A and shows an elevation 
of the line of sight at A of 156.25 -p 3.13 = 
159.38 feet. As the ground at A has an eleva¬ 
tion of 145, the monument must be equal in 


Map-Reading. 


83 


height to the difference between these eleva¬ 
tions, or 14.38 feet. 

In practice, such repeated halving of the dis¬ 
tance is not commonly performed, an estimation 
of the distance being sufficiently accurate. For 
example, having made the first application of 
the base, and found the far end (150) so near A, 
it would be clear that another whole application 
of the distance would be too great, and the pa¬ 
per would be folded as explained, so as to halve 
the base. On trying this new base (whose alti¬ 
tude is 12J), it would be observed that A lies 
about three-fourths of its length—that is, of the 
distance from 150 to 162J. It would only be 
necessary to add to 150 about three-fourths of 
12 \ (= 9.375) to know that at A the elevation 
of the line of sight is 159.375. 

A similar process would show where the line 
of sight pierces the ground, the folding and re¬ 
folding of the paper continuing until the ground 
and the line of sight have the same elevation. 
It is usually close enough in the latter class of 
problems to know between what two adjacent 


8 4 


Map-Reading. 


contours the line enters the ground, for the ex¬ 
act spot is of little importance, and the inac¬ 
curacies of the map will be greater than the error 
thus introduced. 

The last two methods required the use of pa¬ 
per and pencil; but a scale of equal parts or of 
yards and a little mental arithmetic will also 
solve such problems on the principle of similar 
triangles (their sides, it will be remembered, are 
proportional), for we can mentally compare 
their bases. In Plate 15, A is 4 \ contours higher 
than C and B is 2 \ contours higher than C—that 
is to say, the altitude of the triangle at B is 
of that at A (= f). For C to be just visible 
from A it must be at C 7 at a distance from B ex¬ 
actly | of the whole distance from C to A (Plate 
19). The distance is less than f and C is in¬ 
visible. The triangles C'BD and C'AE are sim¬ 
ilar and their bases are proportioned to their alti¬ 
tudes. C 7 is just visible, CB is less than i of 
CA and C is invisible, and C"B is more than f 
of CA and C" is visible. 


Map-Reading. 


85 


E 



Or the relations of the triangles may be 
worked out by the proportion 

Distance to intervening ( . ( Distance from obser-) .. ( Partial ? . < Whole 
object ) ’ l ver to observed point J * ‘ ? rise ) ' } rise. 

Using the figures of the example on page 80 
and Plate 18, C to B = 500 yards, C to A = 1,200 
yards. The proportion becomes 500 : 1,200 
:: 25 feec : 60 feet—that is to say, the line of 
sight at A will be 60 feet higher than at C, or 
160 feet. A being 145 feet, the monument will 
be 15 feet, as before. The small difference of 
0.6 foot is due to the use of different methods, 
and is immaterial in view of the inaccuracy of 
maps in general. 

Before starting on the next step, it would be 
well for the student to practice faithfully and 
persistently the determination of visibility as 






86 


Map-Rsading. 


outlined here. Imagine yourself at a certain 
point on the map, preferably on a hilltop at first, 
and mark the point with a pencil; draw a line in 
any direction, and examine the contours as they 
cross it. Can you see the bottom of the slope? 
How far down the hill would you have to go in 
order to see the bottom? Would “that” hill 
prevent you from seeing ‘ ‘ that town ’ ’ ? Make up 
such questions, solve them mentally, and then 
check your estimate by computation or graph¬ 
ically, as indicated. 

In all work of this character it is well to re¬ 
member that if the observer is at the same height 
as the intervening object, all lower objects will 
be hidden, and that often the deciding factor is 
the contour almost at your feet or just above the 
object at which you are to look, rather than 
some prominent feature which looks “like the 
illustrations in the book.” Remember, too, 
that when looking along a slope contours that 
lie close together at the bottom and wider apart 
at the top show a convex general section, which 
means invisibility; while the reverse conditions 


Map-Reading. 


87 


indicate that the top and bottom of the slope 
are mutually visible. The height of the observ¬ 
er’s eye above the ground, the height of trees, 
houses, and other features shown on the map, 
and the height of the object viewed, all are ig¬ 
nored in this work, unless the conditions of the 
problem especially mention them. 

The next step is the determination of the 
area visible from any given point. In solving 
questions of this character you will use perhaps 
several of the foregoing methods of determining 
visibility, but by far the greatest part of the 
visible area will be determined by inspection 
alone. The work must be systematically per¬ 
formed, and small refinements of location may 
be ignored. 

Mark your station on the map and from it, 
as a center, draw a circle of the ordinary visual 
limits—say two miles. With a pencil, sketch 
in the limiting borders of all areas that are 
plainly visible and those that are evidently in¬ 
visible; this will leave a number of narrow 
strips that are doubtful. Do this work slowly 
enough to be reasonably sure of eliminating all 


88 


Map-Reading. 


but the doubtful areas. Within these doubtful 
areas work out on successive lines the point 
where the line of sight pierces the ground and 
connect these points. As you grow more expert 
in map-reading, the areas to be worked out 
by computation will decrease appreciably, and 
finally you will be able to solve all ordinary 
problems with sufficient accuracy for practical 
purposes by simple inspection. 

Questions as to how much of a given stream 
or road is visible from a given point are solved 
in the same way, but are more simple than those 
involving the limits of vision. 

The foregoing principles involved in visibility 
problems will be made clearer by reference tb 
Plate 20 (Map of Fort Leavenworth and Vicin¬ 
ity)* and the following problems, but, before 
taking them up, a word of caution as to their 
practical value should be given. 

The methods of map-making are such that, 
with even the most accurate of maps, carefully 

* Several small copies of this map accompany the book, that the 
student may use in solving visibility problems, and thus avoid 
defacing the larger map. 



Map-Reading. 


89 


surveyed in time of peace and made on a fairly 
large scale, contours will often be found to be 
incorrectly placed, and many incidents of the 
ground that are large enough to affect the ques¬ 
tion of visibility are too small to be shown at the 
scale of the map, and are therefore omitted. 
Again, trees, hedges, underbrush, growing crops, 
etc., exist in nature that are not shown on the 
map. It is clear, therefore, that where the solu¬ 
tion of a visibility problem shows a very small 
difference between visibility and invisibility—a 
frequent case in the theoretical problems with 
which we have been working—-no practical re¬ 
liance could be placed on the result. Yet many 
practical uses of this class of map-reading prob¬ 
lems will arise in actual service, where, allowing 
a sufficiently large margin for the confessed limi¬ 
tations and inaccuracies of the map, troops may 
be marched and posted, attacks launched, and 
patrols and scouts directed, hidden from the 
sight of the enemy by the topographical features 
shown on the map and appreciated by a skillful 
map-reader. 


VII. 


Problems in Visibility. 

Fort Leavenworth Map {Plate 20.) 

Question i. — Can an observer at B see the 
northwest corner of the wall of the Federal Peni¬ 
tentiary at C ? 

Answer. —No; he cannot. The hilltop south 
of B (1,060) intervenes and is high enough to 
intercept the view. A sketch section, as explain¬ 
ed on page 77, will show this at once, and it will 
be good practice for the student to make one. 
Meantime, it may be noted that from B to 
the south edge of the intervening hill is 1.7 
inches with a fall of 1 contour, while in the 8.1 
inches from that point to C is a fall of 5 \ con¬ 
tours (1,060 — 950). The lower slope is the 
steeper, the section is convex, and C is not 
visible from B. 


90 




Map-Reading. 


9i 


By the usually adopted method the same re¬ 
sult is obtained, for—taking the distance from 
B to the 1,060 contour on the edge of a piece 
of paper—it represents a drop of 20 feet (1,080 — 
1,060) in the line of sight. The first application 
towards C gives an elevation of 1,040—just 
grazing the 1,040 contour opposite the “S” of 
“Sheridan’s Drive.’’ The next application (= 
1,020) is near the word “Cemetery,” the next 
(= 1,000) on “Long Ridge,” the next (= 980) 
at the railroad. Folding the paper brings the 
first application of the half-base (=970) on the 
860 contour. Another application will evident¬ 
ly go far beyond C, so the paper is again 
folded, representing a fall of 5 feet. The appli¬ 
cation of this base (= 965) is beyond C, 
which point lies about three-fifths of the length 
of the base (= a fall of 3 feet) beyond the 860 
contour. The elevation of the line of sight at 
C is, therefore, 970 — 3 = 967 feet, and C, with 
an elevation of 950, is below it and invisible. 

It will be observed that the first application 
of the base (1,040) falls on the 1,040 contour, 


^>2 


Map-Reading. 


showing that a line grazing the ground at the 
point selected for “the intervening point’’ also 
just grazes the ground at the 1,040 contour. A 
very slight change of either the base or the posi¬ 
tion of the 1,040 contour would make this the 
intervening feature, and not the 1,060 contour 
selected. The advantage of this method of de¬ 
termining visibility is thus illustrated in that, 
like the system of drawing a section, the ground 
may be examined all along the line of sight for 
possible points of interference, an advantage not 
possessed by the other methods. It is more 
convenient than the “section” system, and yet 
possesses almost the same virtues, and it should 
now be clear to the student why map-readers 
prefer this method to others which seem easier, 
such, for instance, as the following: 

The intervening feature is 5.5 contours and 
B is 6.5 contours higher than C; and the distance 
from C to the intervening feature is not of the 
distance from B to C. (-|f of 9.8 inches = 8.3 
inches.) 

Or, again, the distance from B to the 1,060 



Map-Reading. 


93 


contour is 766 yards and from B to C is 4,340 
yards. Now, the drop in the first distance is 
20 feet, and from the proportion 766 : 4,340 :: 
20 : 113.3 it is seen that at C the line of sight 
would have an elevation 113.3 feet less than B. 
(1,080 — 113*3 = 966.7.) C is 16.7 feet below 
the line of sight and is invisible. 

It should also be observed that in the solu¬ 
tion of this problem the hill south of B was taken 
as being at and having the elevation of the 
farthest crossing of the top contour (1,060). 
This is usually the method of determining the 
height and location of the intervening point 
where the location and elevation of the highest 
point of the hill is not given in figures. It is 
based on the assumption that the last element 
of the hill above the top contour has the same 
slope as the line of sight or that it has a gentler 
slope. Since neither the height of the observer’s 
eye above the ground nor the size of the object 
observed is considered, this assumption may 
safely be made. Whenever, in a problem, this 
would be evidently untrue, or a closer approxi- 


94 


Map-Reading. 


mation to the slope and position of the high 
ground within the top contour can be made, the 
usual assumption given here would, of course, 
stand aside for the better one. 

Question 2. —Can an observer at B see the 
top of the Catholic church steeple atDf 

Answer. —Yes. The contours indicate a 
concave general section, but the hill 880 lies be¬ 
tween and quite close to one end of the line of 
sight, and this is a condition which usually de¬ 
mands consideration because of the marked ef¬ 
fect on the line of sight which even a slight rise 
produces, if that rise occurs near one end of the 
line of sight. 

In this problem the height of D (900) 
makes it unnecessary to consider the 880 hill, 
which is clearly below D, Whether the ob¬ 
server at B could see the bottom of the 
church (855), however, is not so apparent, but 
by drawing a section or by successive applica¬ 
tions of the base from B to the hill 880 it will 
be seen that the bottom of the church is just 
visible. The whole base is so large that the 


Map-Reading. 


95 


paper is at once folded three times, giving eight 
divisions, each of which represent a fall of one- 
eighth of 200 feet = 25 feet. The first applica¬ 
tion of this base falls on the church with an ele¬ 
vation of 855; or, the rise from the church to 
the 880 point is 25 feet; from the church to B 
is 225 feet and the shorter distance is just ^ 
(= 4 ) of the whole distance from B to D. 

Question 3. —An outpost has patrols at 4, 5, 
and 6; a hostile patrol at A observes one of 
these patrols. Which patrol was seen f 
Answer.- —The patrol at 5 was seen. 
Considering the patrol at 4: To see this patrol, 
the patrol at A must look over the flat sur¬ 
face along the road included in the 860 contour. 
This is the same elevation as at A, hence any¬ 
thing on a lower elevation is hidden; 4 is 90 feet 
lower (770) and is invisible. 

Considering the patrol at 5: As before, the 
860 contour hides all below it, but 5 is above 
860 (it is 890) and may be visible. We ignore 
everything below 860, and so have nothing to 
consider except the ground immediately in front 


9 6 


Map-Rkading. 


of 5 (above the 860 contour). This has a con¬ 
cave section, and 5 is visible. The patrol at 6 
can be dismissed from consideration, as it is be¬ 
low 860. 

Question 4.— An outpost has sentinels at 1, 
2, and 3. A hostile patrol , moving from Schuef- 
fer’s house along the route indicated by the dotted 
line was first seen as it crossed the Millwood Road. 
Which sentinels saw the patrol at that point f 
Answer. —The sentinel at 3 first saw the pa¬ 
trol. No. 1 could not, for the 1,000 contour of 
the spur south of Hancock Hill is about half¬ 
way to the Millwood Road, where the line of 
sight would have an elevation, roughly, of 960. 
(1,040 — 1,000 = 40; 2 x 40 = 80; 1,040 — 80 
= 960.) 

No. 2 cannot see the head of the column. 
By inspection we see that‘the same spur is the 
obstacle, if there is any. A line drawn in the 
direction of the head of the column and tangent 
to the spur crosses it at an elevation of 930, 115 
feet below No. 2 and 5 inches from him. The 
remaining distance to the head of the column is 


Map-Reading. 


97 


3.2 inches, so the line falls in that distance - 5 - of 
115 feet = 73.6 feet. The line then has an ele¬ 
vation of 856.4 feet at the head of the column, 
and as the head of the column itself at this point 
has an elevation of only 850, it cannot be seen by 
the sentinel at No. 2. 

No. 3 can see the column, for while it ap¬ 
pears that the same spur may interfere, a closer 
inspection shows that it does not. The line is 
tangent to it at an elevation of 900 feet, 120 feet 
below and 6 inches from No. 1. The remaining 
d-.stance is about 3 inches, at which point the 
line is I of 120 or 60 feet below 900, and has an 
el rvation of 840 feet. The head of the column 
al 850 feet can be seen by No. 3. 

Question 5.— What point on the north-south 
road had the column of the preceding problem 
reached when it was visible to all of the sentinels f 

Answer. —Such a problem might, under 
some circumstances, be very difficult and even 
indeterminate, but in this case it is not difficult. 
The obstacle to sight, considered in each case, 
has been the same spur and it has interfered 


9 8 


Map-Reading. 


with No. i more than with the others. If we 
find a point where this spur no longer prevents 
No. i from seeing the column, it is probable 
that both of the other sentinels wall be able to 
see it at this same point. If we place the head 
of the column about .25 inch south of the north 
branch of the 840 contour on this spur, No. 1 
can see it. 

Pivot a rule on the observer’s station (No. 1) 
and make it tangent to. the nose of the 1,000 
contour. In this line the patrol on the road will 
have an elevation of 870 and be invisible. Tan¬ 
gent to the 980 contour the patrol has reached 
the stream 860 and is still hidden; tangent to 
the 960 contour the patrol is at the 940 and is 
still hidden. For the first time it becomes visi¬ 
ble to No. 1 about .25 inch south of the 940 con¬ 
tour. It is also visible to Nos. 2 and 3 at this 
point, and hence for the first time visible to all. 

It will be remembered that in such problems 
the general rule is that, when the map shows 
that we can just see or cannot see from one point 
to another, or where the decision could be 



Map-Re;ading. 


99 


changed by a slight change in the height or form 
of the contour, no map is sufficiently accurate 
to allow an important decision to be made on 
such information. However, many points as to 
visibility may be safely settled with even a good 
military sketch when it is evident that a consid¬ 
erable difference between the map and the 
ground would not affect the truth of the decis¬ 
ion. The omission from consideration of woods, 
which is here allowed, would not, of course, be 
justified in actual practice. Their position and 
estimated height would have to be considered 
exactly the same as intervening high ground. 
If, however ,the trees were scattered, it might be 
seen that they would not make a perfect screen, 
and the result might show that if a tree were just 
in line so that it would interfere with the sight, 
a movement of a few feet by the observer would 
enable the distant object to be seen by him. 

Question 6. —How much of the Millwood 
Road can be seen by an observer standing on the 
figures 1,060, 300 yards N. N. W. of B ? 

Answer. —It is visible throughout its length. 


IOO 


Map-Reading. 


From the edge of the Military Reservation (dot¬ 
ted N.-S. line) to Salt Creek the observer is look¬ 
ing along a concave slope. From the creek to 
the hill at Taylor’s he is looking over a valley 
(concave); from Taylor’s to the edge of the map 
is probably visible in the absence of data suffi¬ 
cient to determine the exact slopes on the 
hilltop. 

Question 7. —What extent of country would 
be visible to a man standing on Engineer Hill {at 
E) if it is assumed that the woods are correctly 
shown and that they are thick enough to interfere 
with vision and are of an average height of 40 feett 
Consider the observer s eye as 5 feet above the 
ground. 

Answer.— In the solution of such problems 
the results are obtained largely by the determ¬ 
ination of two points on the line of sight—the 
point of tangency, which we have called the “in¬ 
tervening object,” and the point where the line 
of sight pierces the ground. The first of these 
usually can be recognized by inspection, the sec¬ 
ond by the methods previously discussed.. The 



Map-Rkading. 


ioi 


problem of determining the point of tangency is 
a little different from the simple case of visi¬ 
bility, heretofore explained, in that, no longef 
having a definite line connecting two points at 
the ends, we usually determine the direction of 
the trial lines of sight by an arbitrary choice of 
the intervening feature; as where, in determin¬ 
ing the area hidden by a spur, we try successive 
contours, as we did in Problem 5 (q. v.). 

Under the conditions of this problem the 
woods are too dense to be seen through, hence, 
with a blue pencil, we can block out all woods, 
the ground within the woods being invisible. 
Stick a pin at E and pivot a ruler on it; move 
the ruler tangent to the east edge of the woods 
southwest of the National Cemetery, and draw 
a line to the E. S. E. Similarly mark the area 
hidden by the woods on south Merritt Hill to 
the southwest and east toward the Rock Island 
bridge. Block out the hidden area. Move the 
ruler to the west end of the buildings near Kear¬ 
ney Avenue and draw a line northward from the 
buildings. These buildings will hide everything 


102 


Map-Reading. 


behind them, being on high ground. Similarly 
draw a line tangent to the west and another to 
“the east end of the barracks on Pope Avenue. 
Follow the south and west faces of the buildings 
on the West End Parade with a blue pencil, and 
you can block out as invisible all of the ground 
hidden by the buildings. Draw a line down the 
nose of North Merritt Hill from about the middle 
of the barracks to Grant Avenue at Merritt 
Lake. The east slope of this hill will be hidden 
and the valley beyond to about the 840 contour. 
The 860 contour on Engineer Hill will hide the 
slopes of that hill and the stream-lines at their 
bases; Merritt Lake will also be hidden, except 
the east end; the crest of South Merritt Hill 
will hide all beyond; similarly, the hilltop 870 
will hide what is behind it as far as the slope 
near Atchison Cross, and the pivoted ruler, just 
touching this 870 contour, marks the limits of 
the hidden ground. Where the eastern limiting- 
line crosses the south slope at the 860 contour 
the invisible portion spreads to the east in the 
valley, keeping a little below the 860 contour as 





MAP-RlvADING. 


103 


far as the nose, where it joins the invisible area 
on the northern fork of the stream. The east 
end of the top of Long Ridge will be visible, also 
a portion of the garden and apparently a portion 
of the target-range. 

In a general way we may thus block out the 
greater part of the hidden area, leaving but lit¬ 
tle to be worked out, such as the boundaries of 
invisible portions where not wholly apparent, 
etc. 

Considering the doubtful part of the Target- 
range: The woods ^outhwest of the National 
Cemetery will hide all behind them as far as the 
next invisible portion in the woods near the 
railroad-cut, for the elevation of the lowest trees 
is 40 feet + 880 = 920 feet, and the line of sight 
is inclined upward, increasing this elevation 
rapidly. 

Draw the first test-line tangent to the nose of 
the 900 contour just above the letters “rd” of 
“garden. ” From E to this point is a rise of 25 
feet; therefore this line, beyond the point of tan- 
gency, is higher than 900, and so higher than any 


io4 


Map-Rkading. 


part of the target-range, and the blocked-out 
portion may be extended to the new line beyond 
the point of tangency. Draw a similar line tan¬ 
gent to the same spur at the 880 contour (be¬ 
low “ar” of “garden”); this shows a rise of 5 
feet (880 — 875) in 2.4 inches, or feet in to 
of an inch. By the scale of tV inch on the ruler 1 
we can count beyond the point of tangency tt 
of a foot for each graduation until ground and 
line of sight are equal. 

The falling ground beyond the tangent point 
shows that the ground is hidden, and allows us 
to skip from that point to, say about the 4-inch 
mark. This gives us: 


Point. 

Elevation of Line of 
Sight. 

Elevation of Ground. 

Tangent Pt. 

880 

380 

Tangent Pt. plus 1.6 inches. 

88334 

892 (estimated). 


The line of sight is “ in the ground ’ ’ and that 
point is visible. An examination of the shape of 
the contours indicates that Long Ridge extends 
its influence into the target-range, so we select 
the next point on the line of sight as being at the 
intersection of the ridge and the test-line with an 








Map-Reading. 


105 

elevation of 890 (estimated). This point is 1.3 
inches from the 880 contour (point of tangency) 
and shows an elevation of 882.7, 7.3 feet “ in the 
ground.” From here to the crossing of the 880 
contour the slope is uniform; at that contour 
(0.8 inch = 881.7) the line of sight is 1.7 feet 
above the ground. The exact point of piercing 
which must occur somewhere in the 0.5 inch be¬ 
tween these last two results may be found by the 
proportion:* 9 : 7.3 :: 0.5 : distance from 

*Note.—I t will be seen that the above proportion is: 

Distance above ground, ) ( Distance ) ( Horizontal dist. ) fDist. from 

plus distance below the > : < below the > : bet. high and low > lo ^ ^ of 

ground ) ( ground ) ( ends of line of sight) ( n. o a. 

The pioportion is also true if the second and fourth terms are 
given in terms of the high end of the line of sight, and so long as the 
line of sight between both ends lies over a uniform slope. The gen¬ 
eral proof of this is seen by the following analysis: 

Base measures 5 units (o. 1 inch each). 

Differences of elevation as above are 1.7 feet above the ground 
at the high end and 7.3 feet below the ground at the low end. 

Bet X = distance from high end. 

Y = distance from low end. 

Then X x Y = whole 
distance = 5 units (1). 

X : Y :: 1.7 : 7.3 (2) from similar triangles. 

1.7 X = 7.3 Y.(3) from (2). 

Y^ 5 5 Zx} .(4) from (1). 

Substituting value of X as found in (4), the equation (3) becomes: 





io6 


Map-Reading. 


the 890 point, = 4.06 tenths of an inch. The 
point of piercing, therefore, is about 0.4 of an 
inch from the 890 point, where the elevation of 
ground and line of sight is 882. The correctness 
of this is easily proven, for this point is about 
0.9 inch from the point of tangency, and the 
line of sight therefore has an elevation of 9 x A 
= 1.9 -f 880 = 881.9. The slope of the ground 


8.5 — 1.7Y = 7.3Y. 

9Y = 8.5. 

Y = 0.944. 

Substituting value of Y in (3), as above: 

1.7X = 36.5 — 7.3X. 

9X = 36.5- 

X = 4.056. 

This is shown graphically in Plate 22. The triangle abc is similar 
to the opposite triangle ade and if transposed so that it occupies the 
position CBe, the comparison of the similar sides is facilitated. BD 
= de = 7.3, BC= be = i ; 7, and CD= 9. Y = Y' = Y". The 
base Da = X 4- Y = 5 units. From the properties of similar tri¬ 
angles 9 : 7.3 :: 5 : 4.056 as above, and 9 : 1.7 :: 5 : 0.944. 


C 



The ’exact point of piercing, therefore, lies 0.944 inch from 
the 880 contour, or 4.056 inch from the 890 point, and its elevation 
is 881.888. It is hardly necessary to remark that no map would 
be accurate enough to warrant carrying calculations to this degree 
of exactness. 








Map-Reading. 


107 


shows a fall of 10 feet in 0.5 inch, or 2 feet to 0.1 
inch. The point of piercing is about 4.06 tenths 
from the 890 point and has an elevation of 
881.88, the 0.02 of a foot difference being due to 
coarse measurements. 

In a similar manner determine the several 
points of piercing and connect these; the ground 
between the line thus found and the line of tan¬ 
gent points is hidden. The point of piercing 
may thus be calculated; it may be found graph¬ 
ically by drawing a partial section, as explained 
on page 77 (Plate 17), or in the following man¬ 
ner, using the same example: 

The line of sight at the tangent point had an 
elevation of 880—that is, in 2.4 inches it had 
risen 5 feet. Prolong the line and lay off this 
same distance (2.4) beyond the tangent point; 
this will be a rise of 5 feet more, or 885. From 
the ridge 890 to the 880 contour the ground falls 
10 feet; divide this into two parts, and the point 
of division will fall where the ground has an 
elevation of one-half of 10 feet lower than 890, 
or 885. The mean of these two slopes will be 


io8 Map-Reading. 

the point of piercing. To find the mean, divide 
each into five parts (each part representing i 
foot), and number or letter each. The mean 
will be where two equal elevations coincide. 



(Plate 21.) This work can be done with a light 
pencil on the map. The elevation (and loca¬ 
tion) of the point of piercing is thus quickly 
found, and, as before, it is about 881.9. 

Question 8. —A battery is on the plateau near 
H and wishes to use direct fire against another 
battery coming into action at G. If the muzzles 











Map-Reading. 


IO > 

of the guns are 3 feet from the ground , how far hack 
from the edge of the plateau can the battery retire 
and still use direct fire with the maximum of cover? 
(Note. —Consider the ground on the plateau as 
level between the 1,040 and 1,060 contours.) 

Answer. —The distance from G (1,020.) to 
the edge of the plateau (1,040) is 1,740 yards 
(5,220 feet). The inclination of the line of sight 
is, therefore, 20 feet rise in 5,220 feet, or 
= T-. Since the muzzles are 3 feet from the 
ground, and must lie in the line of sight, they 
must be 3x261 feet =783 feet from the edge, 
or 261 yards. 

Question 9. — A blue column has reached 
Taylor's School-house , marching east on the Mill- 
wood Road , when it is fired on by a blue battery on 
Hancock Hill , which is so posted as to command , 
with direct fire the road from the school-house to 
the bridge over Salt Creek. Where is the battery 
posted? (1 Consider the top of the hill a plateau 
between contours , as before.) 

Answer. —It is evident that the guns must 
be near the 1,060 contour to enable them to fire 


no 


Map-Reading. 


over the steep slope to the bridge. Assume a 
position at the fork of the roads and draw lines 
to the bridge and to the school-house. 

Consider the bridge: Fall, 1,060—770 = 290 
feet in 1,070 yards = tt; therefore the guns will 
be 11 yards from the 1,060 contour. 

Consider the school-house: Fall, 1,060 — 860 
= 200 feet in 2,470 yards = therefore the 
guns will be 37.5 yards from the 1,060 contour. 
The position of the guns may thus be approxi¬ 
mated as on the road and near the figures 1,060. 

However, we must not exaggerate the im¬ 
portance of these theoretical considerations, for 
in reality things are not so simple as this. The 
contours of the ground are not mathematically 
precise, the slopes are not uniformly regular, 
and crests are formed of alternate curved and 
flat surfaces, which completely modify the con¬ 
ditions of defilade. It is, nevertheless, possible 
to make a rough estimate of what is likely to 
happen in action and of the points to which ex¬ 
ecutive officers should direct their attention. 

With the knowledge of map-reading that you 






Map-Reading. 


ii 


now possess, you should be able to describe with 
a certain amount of accuracy the ground that 
would be seen from any point, the probable char¬ 
acter of the roads and of the country passed 
through in going along the roads. Practice 
yourself in this by writing road reconnaissance 
reports, based on the map. A good plan to fol¬ 
low is to assume a march from, say one town to 
another, choosing your route over the shortest 
road and the one best suited to wheeled traffic. 
To do this, draw a line connecting the two 
towns; now look for the road that diverges 
least from this line and which has the gentlest 
grades.* Having chosen your route, begin by 

* Remember that in reducing contours to gradients, both numer¬ 
ator and denominator of the gradient must be in the same unit and 
that the numerator is always i. Thus, if the bottom of a hill has 
an elevation of 800 and the top 920, the rise is 120 feet, and if the 
distance (measured along the road) is 800 yards, the gradient is 
Ho«jt = isV T 3 ° slope. 

The inclination of a road is also sometimes referred to in terms 
of the rise in 100 units, as being “such a percent” slope or grade. 
The grade in the example just given would be a 5 % grade, since 
it rises 5 feet in 100 feet ( 2 ^ = I f Tr ). In that example it will be 
observed that while the gradient is the g ra de is 5 % and the slope 
is 3 0 , all equivalent expressions. 

The character of the road is often indicated by the grades that 
occur on it. A 5 0 slope (y 1 ^) is an excessive grade for a good 
road, even when crossing the mountains, and it is generally con- 



11 2 


Map-Reading. 


describing the point of starting, then go on to 
the next point that should be described, state 
how far it is from the last point, the gradients 
passed over, the nature of the country, and so 
on. The following example will illustrate: 

Example: It is determined to go from the 
new U. S. Penitentiary to the Frenchman’s. 
Between Atchison Cross and Salt Creek village 
you have the choice of two roads: one over the 
col between Atchison and Government Hills, 
and the other almost three-quarters of a mile 
longer, through the railroad cut. The latter 

sidered that is the maximum that should be allowed, and then 
only for short distances. 

A 5 % grade (gV) will reduce the tractile power and speed of a 
horse over that on the level one-half if on a good road, and if this 
grade is longer than ioo yards, the team must stop to breathe. 

The normal load for an Army mule is 1,000 pounds, and this 
he can haul without difficulty on a hard, level road; on a ^ gradient; 
this is equal to imposing a load of 2,000 pounds, and since it is about 
four times as hard to draw a wagon over a dirt road as it is to draw 
the same wagon over macadam, his load will be equivalent on such 
a road to 8,000 pounds, if the gradient is A horse is very near 
his limit of power if drawing 2,000 pounds under favorable circum¬ 
stances of road-bed and grade; hence, on the hill and road just 
discussed the teams would have to be doubled if the hill is at all 
long, and this means a serious loss of time to the train. 

Gradients are of the greatest importance when the wagon is 
ascending the hill, but it is well to remember that on a turnpike 
road g 1 5 is the greatest slope that will allow horses to trot down 
rapidly and with safety. 




Map-Reading. 


113 

has very gentle grades except near the cut, 
where a short gradient of £ must be ascended 
(120T3 — 360 == i ). The grade to be ascended in 
the former is longer, but is only -sV, or about 3 0 
feois = lego" = W; It = 3 0 ) , and the shorter road 
is chosen. 

Starting at the northeast corner of the new 
U. S. Penitentiary— 

(1) Cross-roads; N. via National Cemetery 

(2,000 yards) to Fort Leavenworth; S. E. 
via Grant Avenue (1,500 yards) to Leav¬ 
enworth; W. to Salt Creek village, 1.9 
miles. (Route taken.) Surrounding coun¬ 
try open and gently rolling; Corral Creek, 
flowing east, 550 yards N.; buildings in 
Post (i§ miles) visible; new U. S. Peni¬ 
tentiary brick walls, 40 feet high, about 
250 yards square. 

(2) Atchison Cross; distance from (1) 1,200 

yards; road from (1) to (2) rises I for 
first 30 yards, then falls for 600 yards, 
then is level for 250 yards, where spur 
track from U. P. Railroad to Penitentiary 


Map-Re: ading. 


114 


is crossed, it then ascends 3V for 250 
yards, crossing the A., T. & S. F. Railroad; 
the last 70 yards has a gradient of iV. 

The road is everywhere commanded by 
Long Ridge, 1,100 yards north of and par¬ 
allel to road. 

Cross-roads; S. 1,100 yards to Metropol¬ 
itan Avenue; N. to target-range and 1,400 
yards to road through railroad cut to Salt 
Creek; 2,200 yards to National Cemetery, 
and 2 miles to Post; N. N. W. 1,700 yards 
to Salt Creek. (Route taken.) 

(3) Col, 650 yards north of Government Hill, 
distant from (2) 860 yards; road from (2) 
to (3) rises 400 yards at then for 230 
yards at tV, next 150 yards at A, last 60 
yards nearly level; ground within Reser¬ 
vation hidden by trees except narrow 
strip in prolongation of road; Salt Creek 
valley visible from Missouri River to 
Frenchman’s, except about 1,200 yards 
hidden by Sentinel Hill (elevation 1,020), 



Map-Reading. 


15 


a heavily wooded narrow hill, distant N. 
N. W. about 1,000-1,500 yards; etc., etc. 

The above is sufficient, perhaps, to show how 
the map should be studied. The chief point to 
be remembered is to try and imagine that you 
are actually going along the road and making a 
reconnaissance report on it. 

Placing Troops on the Map. 

There is one other use of a map indoors that 
should be understood. In map problems and in 
some special reports you will be required to in¬ 
dicate on the map the exact location of certain 
troops and in this there are two common errors 
that the' student should learn to avoid. The 
first is occupying more room laterally than the 
given body of troops would actually occupy, or 
the reverse condition: showing them as occu¬ 
pying a smaller space than they would actually 
cover. The second is drawing them so timidly 
and unobtrusively that they are perceptible only 
after diligent search. 


Map-Reading. 


i 16 

In placing troops, then, always draw them to 
scale, avoiding the errors of over-extension and 
of under-extension, and make the block repre¬ 
senting the troops thick enough in the direc- 


4 P t 


INPANTRY 

SENTINEL 

COMMANDER. 

IN CHIEF. 

Y 

CAVALRY 

VIDETTEr 


K 

11/54 

34-11 


SECOND BATTALION 

FIRST AND THIRD 

BATTERY " b ” 

OF THE- 54** INFANTRY 

SQUADRONS 54** CAV 

5 * ARTILLERY 


Plate 23 . 



tion of depth to be clearly seen. Draw your 
own troops in bright blue, hostile troops in 
bright red, and, in the same colors, write clear¬ 
ly opposite each body the designation of the 
troops which it represents, as “III. / 54” for 
“Third Battalion, 54th Infantry.” (The shape 






Map-Reading. 


117 

of the block will show whether infantry, caval¬ 
ry, or artillery.) Use Roman figures for bat¬ 
talions, squadrons, corps, and armies, and use 
Arabic figures for regiments, brigades, and di¬ 
visions. (Plate 23, and Fort Leavenworth Map, 
Plate 20.)* 


Examples. 

Ill . / 15 (to represent the second squadron of the 
15 th Cavalry, the second battalion of 
the 15 th Infantry, or the second bat¬ 
talion of the 15th Artillery—according 
to the shape of the block). 

II. Corps ( or simply II. in large letters, where no 
misunderstanding will result). 

{ Cavalry, ) 

Artillery! 1 ^ eSS the 

second battalion— i. e., the first and 
second battalions of the < 4th \ infantry, 

J tArtillery. ) 

*The troops are shown on the map as prescribed in par. 331 
1. D. R., ’04, and illustrate the method of placing troops on a map. 
No tactical deductions should be drawn from their arrangement. 



118 


Map-Rkading. 


2 Brig. 

3 Div. 

2 Div., III. Corps, etc., etc.* 

Practice in placing troops on the map is valu¬ 
able in that you will soon be able to estimate by 
eye the extent of front occupied by a deployed 
battalion, squadron, regiment, etc., and the 
length of the several units stretched out on a 
road. This facility is of great practical value 
in map maneuvers and m actual service. 

*The abbreviations used are definite and cannot be misunder¬ 
stood. Lack of space on a map, together with the necessity of 
using large figures and letters, compels the use of these abbre¬ 
viations, rather than those used and appropriate for orders and 
messages 





VIII. 


Map-Reading in the Field. 

Map-reading in the field is not essentially 
different from the same thing indoors. It con¬ 
sists chiefly in ability to orient the map, to find 
one’s place on the map, to recognize features 
shown on the map, and in an ability to use the 
map as a guide when traveling in unknown 
country. These and the problems already dis¬ 
cussed constitute map-reading in the field. 

Orienting the Map .—The direction or bearing 
of one line from another must be determined 
and expressed with reference to some other di¬ 
rection-line, and the reference-line on maps is 
a north-and-south line, called the ‘'meridian”; 
but .there are two meridians or north-and-south 
lines at almost every place on the earth: one, 
the true meridian, which is unvarying, lying 
always in the same direction and joining the 


119 


120 


Map-Reading. 


place with the North Pole; the other, called 
the “magnetic meridian,” joins the place with 
the magnetic pole. These two lines may differ 
very widely and in Alaska do differ by as much 
as 40°. The existence of these two reference¬ 
lines causes some confusion in map-reading in 
the field, since maps are drawn sometimes with 
reference only to one and again with reference 
only to the other. A military sketch made 
with a compass will have it on a magnetic me¬ 
ridian, which may “point” in quite a different 
direction from the meridian found on a survey 
of the same piece of ground. 

The needle of the compass always points to 
the magnetic north, so that in so far as its limited 
length permits it establishes a visible portion of 
the magnetic meridian at the place, and we can 
therefore, with its aid, actually see the magnetic 
meridian and measure from it the bearings of 
the various objects shown on the map. We 
cannot, however, see the true meridian so easily, 
and hence, on the ground, we are driven to use 
the convenient compass and needle. In those 


Map-Rkading. 


121 


few favored places where the true and the mag¬ 
netic meridians are identical this will make no 
difference, for the needle will then point to the 
true north and we can see the true and unchang¬ 
ing meridian; but in the vast majority of cases 
the needle will point to one north, the meridian 
on the map to another, and the result is the 
confusion referred to. 

Now, the North Pole is fixed and immovable, 
but the magnetic pole wanders about, carrying 
with it the north ends of all the magnetic nee¬ 
dles throughout the world; it moves, however, 
so slowly and with such regularity that map- 
makers can compute its position for any given 
date and place, or, by establishing a true north- 
and-south line by astronomical observations, can 
compare it with the position of the needle at any 
time for that place. Maps, for convenience, are 
usually made with the magnetic meridian; the 
true meridian’s position with reference to the 
magnetic is determined, the true meridian 
drawn and the magnetic meridian erased, thus 
leaving a direction-line on the map that will not 


122 


Map-Rkading. 


change with the passing years. The user of the 
map, wishing to read the map on the ground, 
and with the aid of a compass, does so through 
a knowledge of the relative positions of the two 
meridians—the one that he can see on the com¬ 
pass and the one given on the map—-for the date 
and place when the map is to be used. 

The magnetic meridian may lie either to the 
east or to the west of the true meridian and its 
angular distance from that meridian is called the 
‘ ‘ variation of the compass, ’ ’ the ‘ ‘ declination of 
the needle,’’ and also the “magnetic declina¬ 
tion.” In 1908 the variation in the eastern part 
of Maine is 21 0 west, in the western part of 
Alaska it is 40° east. An officer in Maine, hav¬ 
ing a U. S. Geological Survey map (whose verti¬ 
cal side lines are true north and south) would 
set the N. S. line of his compass-box on the N. S. 
border line of the map and revolve map and' box 
together until the needle pointed to 21 0 west of ! 
the true meridian (Plate 24, a ); while, were he in 
Alaska, he would turn map and box until the 
needle pointed to 40° east of the true meridian 


Map-Reading. 


123 


(Plate 24,6).* In these positions the maps 
would be “oriented”; the east on the map 
would be toward the real east, and everything 


N 


N 



Plate 24 


shown on the map would lie in its proper rela¬ 
tion to the same features on the ground. If the 
map were placed in a straight road and oriented, 
the plotted direction of the road would coincide 
with the actual direction, and one looking along 
the mapped road would see the true road as 

*Do not allow the reversed marking of the cardinal points on 
the compass circle to confuse you in this. Have the needle point¬ 
ing to the actual E. or W. of the true meridian as indicated in 
Plate 24, [a) and (6). 






124 


Map-Reading. 


though it were a continuation of that shown on j 
the map. If the map has a magnetic meridian | 
on it, it is oriented at once and without diffi¬ 
culty by adjusting the N. S. line of the compass- 
box to this meridian and turning map and box ; 
until the needle lies at the north point or zero; 
but if the map has only a true meridian, it will 
be necessary to find the declination before it 
safely can be used in the field. In sketching 
and in map-making this declination must be 
ascertained with some accuracy, but in map¬ 
reading it will be sufficient if you can determine 
it with only a fair degree of accuracy. This can j 
be done if you stand in some clearly identified 
stretch of straight road and turn the map until 
its plotted position coincides with the road in 
which you are standing. The map will then be 
oriented, and, placing the N. S. line of your 
compass on the true meridian, you can read at 
the north end of the needle the declination for 
that place and date. A magnetic meridian 
drawn from the information thus obtained will 
enable you to orient the map at any other place 




Map-Reading. 


125 


in the vicinity in the manner above directed for 
a map which has a magnetic meridian. If you 
can identify your position on the map—as, for 
example, where you are standing at a cross¬ 
roads, which is shown on the map—you may 
orient the map by turning it until some other 
easily identified place, such as a prominent hill, 
a church, etc., that is shown on the map, lies in 
the same direction on both map and ground. 
With the map oriented, determine the declina¬ 
tion as directed. 

Identifying One's Place on the Map .—Usually 
this is easily done by estimating or measuring 
the actual distance and direction to some easily 
identified feature shown on the map and then 
plotting the distance in the reverse direction 
from the plotted feature; but it may be neces¬ 
sary to resort to a rough application of a plane- 
table method of resection. Orient the map, 
draw pencil-lines from the representation of two 
visible plotted points towards you; their inter¬ 
section will be at the point where you are stand¬ 
ing. Any application of the ‘ ‘ three-point prob- 


126 


Map-Reading. 


lem” also may be used, but in practice the map 
is oriented and your position identified without 
resort to any more intricate methods than those 
above given. If you have been following along 
a known road, your position on it can be found 
approximately from a knowledge of your rate of 
march by measuring along the road the distance . 
that you estimate you have traveled in the time 
that has elapsed since you last occupied a known 
position. Thus, if marching with an infantry i 
column, you left a certain town at 2:00 p. m., 
you would measure from that town, along the | 
road traveled, 2 \ miles (or 3 miles, according to 
your rate of march), to find your position at 3 :oo 
p. m. 

When it is necessary quickly to orient the 
map and to identify on it the relation between 
your position and some distant object, take up 
the map in both hands, the thumb of one hand j 
on your position, the thumb of the other on the 
distant point, and turn around until the imagin¬ 
ary line connecting your thumbs coincides with 



Map-Reading. 


27 


an imaginary line connecting the two points on 
the ground. 

When using the map in close country, you 
will not be able to see far enough to enable you 
readily to recognize your position, and, though 
you have a good map and a compass, it will be 
astonishingly easy to lose your way unless you 
are intent upon the relations of map and ground. 
In such a case, or in a dense forest or jungle, 
keep your map in hand and approximately ori¬ 
ented. Mark your'progress from time to time 
with a pencil, checking off recognized points as 
you pass-them; keep your eye on the sun or on 
your compass, roughly checking distances as you 
progress and checking off all road-crossings and 
forks, and, if you are the guide of a party, rely 
| on your own judgment rather than heed the advice 
that will be offered when the route appears doubtful. 
Remember that maps are seldom up to date or 
complete, and look out for alterations in roads, 
houses, bridges, etc. 

Always carry your map so that it comes out 
I of your pocket ready for use— i. e ., with the 





128 


Map-Reading. 


printed matter outside and with the part of the 
country on which you are working before your 
eyes as soon as you take it out of your pocket. 
A transparent waterproof envelope or cover for 
the map is a good thing to have, and it is well to 
prepare it with squares lightly ruled, the sides of 
the squares representing a certain number of 
yards on the scale of the map. . j 

Make sure that you have the scale of the map 
well fixed in your head, and have some rapid 
method of measuring distances on the map.* If 
the map is one with only a true meridian on it, 
be sure that you know how it is drawn with re¬ 
spect to the points of the compass. 

* Everyone should know the size of some portion of his hand— 1 
from one line to another, the length of a finger-joint, of the span 
from the thumb to little finger, etc. A good measurement to know 
is the width of the hand at the knuckles, so that the hand, placed ; 
palm down on the map, will cover a known number of yards or 
miles, at say 3 inches to the mile, as well as the number of inches | 
so covered. 





IX. 


Additional Problems in Map-Reading. 

1. Find the R. F. of the following scales: 

5 inches to the mile; 

5 miles to the inch; 

3 inches to 2,000 yards; 

4 inches to 2,000 meters. (1 meter = 
39.37 inches.) 

2. How many inches to the mile in the fol¬ 
lowing scales? 

111 

15840 100000 80000 

3. How many miles to the inch in the fol¬ 
lowing scales? 

1 1 1 

63360 126720 316800 

4. You have a map which you are compar¬ 
ing with the ground; the scale has been tom off 
the map, and in order to draw a scale for it you 
have paced the distance between two objects, 
which are shown on the map as 2.75 inches 


9- 


129 



13° 


Map-Reading. 


apart, and which, from your pacing, you find to 
be 5 5 o yards. Draw the scale of yards. 

5. Construct a scale of yards with R. F. = 

1 

10560 ’ 

6. On a Russian map of Turkestan, of 

which the scale is 4.75 inches to 500 versts, it is 
found that the distance from Kizil Arvat to 
Askhabad is 1.^93 inches. , What is the actual 
distance apart of these places in miles ? 1 verst 

= 1,166.6 yards. Give the R. F. of the map. 

7. Aline 2J inches long on a French map 
is marked 2,000 meters. Using the graphical 
method, draw a scale of yards for use with 
this map. 

Problems on U. S. Geological Survey Map. 

Standisfield (Mass.) Sheet. 

8. Construct a scale of yards for use with 
this map. 

9. What is the direction from New Boston 
to the following places ? 






Map-Reading. 


131 


Cold Spring, Tolland, Simon Pond, 
Southfield, Montville. 

10. What is the distance from New Boston 
to Otis by the most direct road ? 

11. Your compass has only degrees marked 
on it; sighting from Montville to Standisfield, 
the needle reads “236 0 .” What is the bearing 
in “points”? 

12. From New Boston you are ordered to 
“the hill 1 mile N. E. of this point.” Using the 
above compass, what would be the bearing in 
degrees of the hill to which you are to go ? 

13. What is the elevation of the fork in the 
roads at Standisfield? 

14. What is the difference in elevation be¬ 
tween Standisfield and Montville? 

15. Going from South Standisfield to South- 
field, what is the elevation of each of the houses 
passed ? 

16. In going from South Standisfield to New 
Marlboro, what is the slope between the 1,580 


132 


Map-Reading. 


and i,600 contours where you first cross them? 

(a) Using scale of yards; 

( b ) Using scale of inches. 

17. Construct a scale of M. D.s for use with 
this map. 

18. A rise of 200 feet is encountered in a 
map distance of \ mile. What is the slope and 
what is the gradient ? 

19. Can cavalry charge down the road run¬ 
ning north from Standisfield ? 

20. Is the general section from Standisfield 
to Montville convex or concave ? 

21. Is Montville visible from Standisfield? 

22. If you were standing on Seymour 
Mountain, could you see Abbey Hill? 

23. Is Cranberry Pond visible from Tol¬ 
land? 

24. Is Otis visible from North Otis? 

25. Are both hilltops of Cowles Hill visible 
from Standisfield? 

26. Standing on the west top of Cowles Hill 




Map-Re:ading. 


133 


and looking north, could you see the north fork 
of Buck River? What point on the hill beyond 
the river would first be visible? 

•27. How much of Sandy Brook could you* 
see from the same point ? 

28. Show a regiment of infantry deployed 
in one line facing N. E. on the hill between 
South Standisfield and New Marlboro. 

29. Show a regiment of infantry marching 
on this road, the head of the regiment at the 
cross-roads north of Woodruff Mountain. 

30. Show a brigade (F. S. R.), complete with 
trains, marching from West New Boston to Otis, 
the leading element 1 mile south of Otis. 

31. Orient the Standisfield sheet for map¬ 
reading purposes indoors, using the compass. 

32. Orient the map by the border lines if 
the declination is 6§° W. 

33. Orient the map, considering the declina¬ 
tion 20° E. 

34. Set the map with the top in a general 
north direction, as though you had oriented it 


134 


Map-Reading. 


by a road or other feature on the ground, and 
determine the declination. 

35. Choose your road and make a road re¬ 
connaissance report of the route from East Otis 
to New Boston. 

36. Marching 2 \ miles per hour, how long 
would it take to march from North Colebrook 
to New Marlboro. How long after starting 
would you pass South Standisfield ? 

37. What portion of the road from North 
Colebrook to Standisfield would be under artil¬ 
lery fire from a battery on Seymour Mountain? 

38. What is the angle of depression from 
the east top of Cowles Hill to Standisfield? 

39. On what hill within 1 mile of West New 
Boston would you place an observer to best 
observe the country in the vicinity of South 
Standisfield ? 

40. Where is the steepest grade on the road 
from Otis to West Otis and what is the grade at 
that point? 


APPENDIX I. 

Topographical Terms and Abbreviations Thereof Found in 
French and German Maps. 


German. 

French. 

English. 

Abbau. 

Annexe de village. 

Farm - house some 
distance from a 
village. 

Abdeckerei. 

Equarrisage. 

Place for skinning 
dead animals. 

Brauerei. 

Brasserie. 

Brewery. 

Bruch. 

Faille, bas fond 
marecageux. 

Moor, marsh, bog. 

Busch. 

Bois, bouquet 
d'arbres, buisson. 

Bush, thicket, 
copse. 

Damin. 

Digue. 

Dike, dam. 

Denkmal. 

Monument com- 
memoratif. 

Monument, me¬ 
morial. 

Dratseilbriicke. 

Pont sus’pendu, 
(par cables de 
fil de fer). 

Wire rope sus¬ 
pension bridge. 

Eisenquelle. 

Source ferrugi- 
neuse. 

Mineral spring. 

Fahre. 

Bac. 

Ferry. 


135 













136 


Appendix. 


TOPOGRAPHICAL TERMS— Continued. 


German. 

French. 

Engeish. 

Fahrhaus. 

Station du bac. 

Ferry-house. 

Fliess. 

Ru, petit canal, 
fosse. 

% 4 1 

Small brook, rivu- 
ulet. 

Forst. 

Foret domaniale, 

% grande for6t. 

Regularly planted 
f orests (govern¬ 
mental;. 

Furt. 

Gue. 

Ford. 

Gas Anstalt. 

Usine 4 gaz. 

Gas-works. 

Heide. 

Lande, bruykres. 

Heather, moor. 

Hochofen. 

Haut fourneau. 

Blast furnace. 

Kreuz. 

Croix, calvaire 

Cross, wayside 
shrine. 

Kriegsstrasse. 

Route militaire. 

Military road. 

Leimfabrik. 

Fabrique de colie 
forte. 

Glue factory. 

Luch. 

Bas fond mare- 
cageux. 

Swampy bottom, 
land. 

Luftschacht. 

Puits de ventila¬ 

Air-shaft, ventilat- 

- 

tion. 

ing-shaft. 

Massengrab. 

Tombe collective 
(de champ de 
bataille). 

Burial-trench (on 
the battle-field). 













Map-Reading. 


137 


TOPOGRAPHICAL TERMS— Continued. 


German. 

French. 

Engeish. 

Rangierbahnhof. 

Gare de triage. 

Switching station. 

Revier. 

District forestier, 
verderie. 

Forest district, 
verdereris dis¬ 
trict. 

Schiesstand. 

Stand. 

Firing-stand. 

Seilbahn. 

Chemin de fer 
funiculaire. 

Cable road. 

Springgrube. 

Foss6 (pour 1 e s 
exercises de 
sauts). 

Ditch for (jump¬ 
ing exercises). 

Stift. 

Institution re- 
ligeuse. 

Religious institu¬ 
tion. 

Uebungsschanze. 

Retrenchment 
d’exercises. 

Intrenchment for 
training pur¬ 
poses. 

Viehtrift. 

P&turage. 

Pasture. 

Wasserleitung. 

Yqueduc. 

Aqueduct. 

Wehr. 

Barrage.} 

Weir, dam. 

Zollamt. 

Douane. 

Custom-house. 












138 


Map-Reading. 


ABBREVIATIONS. 

--- M 


German. 

French. 

English. 

B., Bach. 

B., Berg. 

Ruisseau. 

Montagne, hauteur. 

Brook, creek. 

Mountain, height 

Baumsch., Baum- 
schule. 

Pepinfere. 

Nursery for young 
trees. 

Begr., PI., Begrab- 
nissplatz. 

Lieu d’inhumation, 
cimetikre. 

Place of interment, 
cemetery. 

Bhf., Bahnhof. 

Gare. 

Railroad station. 

B. W. N.. Bahn 
Warter, No. 

Maison de garde 
barriere, No. 

Crossing-keeper’s, 
hut, No. 

Ch. W., Chaussee 
Warter. 

Maison de can- 
tonnier. 

Road worker’s hut. 

Fab* or Fb., Fabrik. 

Fabrique. 

Factory. 

F. H., Forst Haus, 
Forsterhaus. 

Maison forestiere. 

Forester’s house. 

FI., Fluss. 

Riviere. 

River. 

Fl. Br., Fliegende 
Briicke. 

Pont volant. 

Flying bridge. 

F. P. M., Friedens 
Pulver Magazin. 

Magazin a poudre 
de chasse. 

Magazine for hunt¬ 
ing powder. 

G., Gb., Gebirg. 

Montagnes. 

Mountain. 

Gr., Graben. 

Ru, fosse. 

Channel, ditch. 












Map-Reading. 


i39 


ABBREVIATIONS— Continued. 


German. 

Gr., Graber. 

Gr., Grube. 

Gr., Grund. 

H , Hohe. 

Hgl., Hiigel. 

H. St., Halte 
Stelle. 

I. , Insel. 

Kap., Kapelle. 

K. F., Kahn Fahre. 
Khf., Kirchhof. 

K. P. M., Kriegs 
Pulver Magazin. 

Kr., Krug. 

K. O., Kalkofen. 

Ksgr., Kiesgrube. 

Ks. u. s. Gr., Kies 
und Sand Grube. 


French. 

Tombes. 

Fosse carri^re. 
Bas-fond, fond. 
Hauteur. 

Colline. 

Halte, station de 
chemin de fer. 

lie. 

Chapelle. 

Bac. 

Cimetfere. 

Poudrfere militaire. 

Auberge. 

Fpur k chaux. 

Carrie re de gravier. 

Carri&re de gra¬ 
vier et de sable 


Engush. 

Graves. 

Trench, pit, hole. 

Ground, low-lying* 
ground. 

Height. 

Hill. 

Stopping-place. 

Island. 

Chapel. 

Boat ferry. 

Church-yard, 

cemetery. 

Military powder 
magazine. 

Tavern. 

Time-kiln. 

Gravel-pit. 

Gravel- and sand¬ 
pit. 











140 


Map-Rlading. 


ABBREVIATIONS— Continued. 


German. 

French. 

English. 

Lgr., Lehmgrube 

Carrie re de glaise. 

Clay-pit. 

L. M., Loh Miihle. 

Tannerie. 

Tan-mill, tannery. 

L. u. Mgl. Gr., Lehm 
und Mergel Grube. 

Carrie re de glaise 
et de marne. 

Clay- and mari¬ 
nate) pit. 

M., Miihle. 

Moulin. 

Mill. 

Obst. PI., Obst 
Plantation. 

Verger. 

Orchard. 

0. M., 01 Miihle. 

Moulin a huile 

Oil-mill. 

Pf., Pfuhl. 

Mare. 

Pool, pond. 

P. M., Papier Miihle. 

Papeterie. 

Paper-mill. 

Pv. M., Pulver Miihle. 

Poudrerie 

Powder-mill. 

S., See. 

Lac, etang. 

Lake. 

Schaf. or Schf., 
Schaferei. 

Bergerie. 

Sheep-fold. 

Schl., Schleuse. 

Ecluse. 

Sluice, lock. 

Schl., Schloss. 

Chateau. 

Castle. 

Sgr., Sandgrube 

Carri&re de sable. 

Sand-pit. 

S. M., Ssge Miihle. 

Scierie. 

Saw-mill. 

St. Br.. Steinbruch. 

Carrikre de pierre. 

Stone quarry. 













Map-Reading. 


141 


ABBREVIATIONS— Continued. 


German. 

French. 

English. 

T., Teich. 

Etang. 

Pond. 

Thon Gr., Thon 

Carrfere d’argile. 

Clay-pit. 

Grube. 

T. 0., Teer Ofen. 

Usine k goiidron. 

Tar works. 

Vw., Vorwerk. 

Ferme. 

Farm-house some 



distance from a 
village. 

W., Wald. 

For£t. 

Forest. 

Wasch., Wasch- 

Lavoir. 

Laundry, wash¬ 

haus. 


house. 

Wein B., Wein¬ 

Vignoble. 

Vineyard. 

berg. 



W. M., Walk- 

Foulerie. 

Fullery, cloth-mill. 

miihle. 



Wn., Wiesen. 

Prairies. 

Meadows. 

Z. F. B., Zucker 

Sucrerie. 

. Sugar factory. 

Fabrik. 



Zgl., Ziegelei. 

Briqueterie, 

tuilerie 

Brick-yard. 












APPENDIX II 


Table op the Chief Foreign Measures op Length and Their 
Corresponding Distance in Inches, Feet, and Miles. 


S 

<D 


<u 

s 


f France, 

I Belgium, 

i 

i Italy, 

| Portugal, 
l_ Spain, 
Germany, 


Greece, 

Holland, 

Austria, 

China, 

Denmark 

and 

Norway, 

Japan, 

Philippines, 


Millimetre 


metre. 


1000 

Metre. 

Kilometre 1,000 metres. 


Millimeter or strich 

Meter or stab. 

Kilometer. 


Gramme — millimeter. 

Pecheus — meter. 

Stadion = kilometer . . 


Streep millimeter. 

El = meter. 

Mijle kilometer .. 


Linie. 

Fuss 144 linien. . 
Meile = 24,000 fuss. 


Ts’un (10 fan) . 
Ch’ih (10 ts’un) 
Li. 


Linie. 

Fod — 144 linien. 
Mil 24,000 fod. 


Bu.... 
Shaku. 
Ri . . . 


Pulgada. . . 

Pie. 

Kilometro. 


Inches. 


39371 


.0864 


1.41 


.0858 


.1193 


Feet. 


3.2809 


to t-h c3 

Sh 

0) ^ «4_ 

■ft a O 
CP 

g K5J00 

o «■ II 

JS >»« 

rt lisa 


.927 


Miles. 


.62138 


1.0371 


1.175 


1.0291 


.9943 


.927 


4.7142 


.4005 


4.6805 


2.4434 


.62138 


112 











































































Map-Reading 


M3 


APPENDIX II —Continued. 



Inches. 

Feet. 

Prussia 
(old sys¬ 
tem), 

Linie. 

Fuss = 144 linien. 

Schritt (pace). 

Meile 24,000 fuss. 

.0859 

1.0297 

2.4714 

Russia, 

Vershok. 

1.75 


English foot. 

Arschine 16 vershoks. 

1.00 

2.3332 


Sajene 48 vershoks. 


7.0000 


Verst 500 arschines. 


Sweden, 

Linie. 

.11689 


Fot = 100 linier. 

.9742 


Meile = 36,000 fot. 


Switzerland, 

Linie. 

Fuss = 100 linien. 

.11811 

.98427 


Schweizerstunde 16,000 fuss . 

Kerat,. 


Turkey, 

1.125 


Halebi or archim. 

2.325 


Berri. 







Miles. 


4.6805 


.6628 


6.6416 


2.9826 


1.0386 




































































































































































































































































































PLATE 20 








































































































































































































































































































































































































































































































































































































vs 



c r. 



„ ^ & 

Pd 

O . ^ P- 

" S 1 


*n* 

N> 


^ % 


Vj 

s 


« 
o 
►—> 
< 


K" 

P3 


< 

C/D 



O' 

CJ 


O 

2 : 

M 


H-^ 

K 


CO 


-) 

6 

CQ 

S 

D 


Oh 

v 

| £>H 

H 

r 

I J 

CJ 

: 

C/3 

W 

< 

CQ 

C/3 

£ 

S 

< 

>“H 



2; 


O 


CO 


Q 


D 


b~i 






/ 








I 











U.S.GEOLOGICAL SURVEY 
CHARLES D.WALCOTT, DIRECTOR 

7,3*15' — 


North Oti 


[ 0 OO‘ 


\ Church Hill 


Kingsbury Ml 


-Haley Pond, 


Monterey 


ckson Hil 


Chestn 


Belden Hill 


Dry Hill 


1500 -\ 


J490 


1747 


'loon 


|Xtt *0 


1634 


1 * 00 - 


Clowles Hill 


Sand.iafi.ehl 


'ninberry Pan 


■!3f4, 


MAS SJi: H IT s E TTS 

v c o njoeT;t:ic tjt 


bound ary 
uX~KH ' ' 


ELRKSHIRE Cf 
LIT C HF 


HAMPDLISr.L/OO 

-C*/ ——M-« Ml 


; l 

^ Ball Ml 


North 

Colebrook 


A 2”00 [ 
,73 i 5’ 


73 00' 


WirtSte-d) 


Settle «rWs 


it MileH 


interval 


]>axujii is mean sea level 











































































































































\ 





























































































































































































































































































































































































































































































































































































































































































































































































































































































































































